SAN FRANCISCO -- Starlin Castro is making progress on his defensive play. Since April 21, the Cubs shortstop has made two errors, and he has one since May 5.

"His development is basically two things in a nutshell -- keep preparing like he has and understand the preparation," Cubs manager Dale Sveum said of Castro, who led the National League with 29 miscues in 2011. "It's preparation that has helped his defense over the last month or five weeks."

Castro has improved on his throws, which is something Sveum has worked with the shortstop on.

"He's playing at a very high, confident level now, and I think a lot of that has to do with the way he's preparing during the day," Sveum said.

What Castro didn't know, until a reporter told him after the Cubs fell to the Giants, 4-3, on Friday, was that his name had been mentioned as possible trade bait in a USA Today story. Both Sveum and Theo Epstein, Cubs president of baseball operations, have said the report was incorrect.

"I didn't even know that," Castro said, sounding surprised. "If I knew that, maybe I'd think about it."

The 22-year-old infielder wants to stay with the Cubs and be part of Epstein's foundation to build from.

"That's what I want, to be here for all of my career," Castro said. "I don't want to go anywhere."

Bowden designated as Cubs claim Asencio

SAN FRANCISCO -- The Cubs bullpen got a new arm on Friday as the team claimed right-handed pitcher Jairo Asencio off waivers and Michael Bowden was designated for assignment.

Asencio, expected to join the team Saturday, posted a 5.96 ERA in 18 games with the Indians, giving up 17 earned runs on 27 hits (including four homers) and eight walks over 25 2/3 innings. He came up in the Braves system and was traded to the Indians on March 29 for cash considerations, then designated for assignment on May 28.

"It's a good arm from Cleveland, who put up some impressive Minor League numbers the last couple years," Cubs manager Dale Sveum said Friday.

Asencio, who turned 29 last Wednesday, is 1-2 with a 6.05 ERA in 27 Major League relief appearances with the Braves in 2009, 2011 and Indians this year.

James Russell is the only left-hander in the bullpen now. Did the Cubs consider adding another, like Scott Maine who is at Triple-A Iowa?

"When those guys prove they can consistently throw strikes [they'll come up]," Sveum said. "That's something we have to do in this organization is make guys understand that consistency is everything and consistency of throwing strikes is something we have to have."

Bowden, 25, an Illinois native, had a 7.45 ERA in 10 games with the Cubs, giving up eight earned runs on 14 hits and five walks over 9 2/3 innings. He had appeared in two games with the Red Sox and given up one earned run on two hits in three innings.

The Red Sox designated him for assignment on April 15, and the Cubs acquired him April 21 to complete the Marlon Byrd trade. In eight games in May, Bowden had a 9.95 ERA, giving up seven runs on 11 hits and three walks over 6 1/3 innings.

Sveum responds to trade-mill report

SAN FRANCISCO -- Manager Dale Sveum was surprised at a report in USA Today that said the Cubs were "letting teams know that nearly everyone but starter Jeff Samardzija is available."

"I didn't read it, but I've heard about it, obviously," Sveum said on Friday. "I think it's absurd for somebody to even write something like that. Some of it might be warranted, and some of it isn't even close to what we're going to do with this organization. You talk about the ultimate skepticism, that's what it is. I think Theo [Epstein] took care of that himself."

Epstein, president of baseball operations, has denied the Cubs were making players like Starlin Castro available.

The Trade Deadline is July 31, which means there will be more rumors.

"The job we have to do has nothing to do with what the media talks about and who's going to get traded and all that," Sveum said. "Your job is to come out here and prepare to do the best you can and win a baseball game. You don't have control over all [the rumors]."

The Cubs have made changes since the season began, such as dealing Marlon Byrd and moving Carlos Marmol out of the closer's role. They began Friday's game 18-32, which is not what Sveum envisioned.

"Did I expect to be 15 games under .500? Of course not," he said. "I don't care what -- if you're rebuilding or anything. You think about each game and winning the ballgame that day. You don't think about rebuilding. That's not my job. My job is to do the best I can with the players I have on an everyday basis."

Cubs work out two potential Draft picks

SAN FRANCISCO -- The Cubs have the sixth pick in the first round of Monday's First-Year Player Draft, and manager Dale Sveum got a first-hand look at two potential selections, shortstop Carlos Correa and pitcher Max Fried, during a workout at Wrigley Field on Wednesday.

"Those are two impressive high school kids," Sveum said on Friday.

The Cubs' manager took part in the workout, throwing batting practice to Correa, a right-handed hitter from Puerto Rico.

"It was pretty impressive to [see him hit to] all three fields in a 20 mph wind at Wrigley Field in batting practice -- straightaway center, right field and obviously, left field," Sveum said.

At 6-foot-4, 190 pounds, Correa resembles a young Alex Rodriguez.

"I played with A-Rod when he was 19, and there were a lot of the same actions, the same body, the same power," Sveum said. "They told me to start working him away [during batting practice], and he started putting them in the seats in right field into a 20 mph wind."

Fried, a left-hander, showed off his arm strength by throwing from deep in right field to home.

"Let's hope one of them is around by the sixth pick," Sveum said.

Dunston talks son's tenure as Cubs prospect

SAN FRANCISCO -- Former Cubs shortstop Shawon Dunston is keeping tabs on his son, Shawon Dunston Jr., who was the Cubs' 11th-round pick in last year's First-Year Player Draft.

Dunston Jr. was still playing at extended spring training in Mesa, Ariz., and had yet to be assigned to one of the Cubs' Minor League affiliates. He will most likely play for Class A Boise.

"He's learning a lot," said Dunston Sr., who is on the Giants' coaching staff. "He's learning these guys are good and he's learning these pitchers throw breaking balls in fastball counts. [My son] said, 'The main thing is I'm learning about myself as a player.' I said, 'There it is.'"

That's something Dad can't teach.

"He's eager," Dunston Sr. said. "They're all eager. That's good."

What's funny is that Dunston said his son and all the other Cubs Minor Leaguers are asking the same question a lot of fans ask: Why isn't Anthony Rizzo in the big leagues? Rizzo, Triple-A Iowa's first baseman, leads the Pacific Coast League with 17 home runs, although he has not played since Sunday because of a sore right wrist.

"Every Minor Leaguer in the Cubs organization is rooting for Rizzo," Dunston Sr. said. "They say, 'Why isn't he up? He's got [17] homers?'"

It's another lesson for Dunston Jr. and the other Minor Leaguers to learn. Cubs manager Dale Sveum doesn't have first baseman Bryan LaHair working in the outfield yet to make room.

"The day Rizzo comes here, he's going to play every day," Sveum said on Friday. "Whatever we do, who really knows? There's nothing you can do about moving people around until he gets here."

Cubs honor prospects Rizzo, Francescon

SAN FRANCISCO -- Triple-A Iowa first baseman Anthony Rizzo and Class A Advanced Daytona pitcher P.J. Francescon were named the Cubs' Minor League Player and Pitcher of the Month for May.

The 22-year-old Rizzo -- ranked by MLB.com as the No. 32 prospect in baseball entering the season -- batted .326 with nine doubles, a triple, 10 home runs and 23 RBIs in 26 games with Iowa in May. His 10 home runs were tied for the most in the Pacific Coast League, while his league-leading .758 slugging percentage contributed to a 1.160 OPS that ranked second in the league.

Francescon, 23, combined to go 3-1 with a 2.58 ERA and a complete game in six starts between Class A Peoria and Daytona. He limited hitters to a .187 batting average and struck out 26. He began the month with Peoria, going 3-0 with a 1.71 ERA in four starts, then was promoted to Daytona on May 21.