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06/26/12 8:52 PM ET

With Rizzo up, eyes turn to Vitters and Jackson

CHICAGO -- Now that Anthony Rizzo has been promoted to the big leagues from Triple-A Iowa, who's next?

Among the players the Cubs are keeping their eyes on are outfielder Brett Jackson and third baseman Josh Vitters.

"I think you have to earn it," general manager Jed Hoyer said Tuesday. "You have to earn getting up here as a Minor League player. Anthony forced our hand, there's no question. He put up as good numbers as any player in the Minor Leagues.

"Players shouldn't get promoted based on Draft status, based on trades," Hoyer said. "I don't think we could look our players in the eye if Anthony hit .250 and hit nine homers and we promoted him to the big leagues. Now you look at his numbers and what he did and it's pretty much impossible to argue with the fact he earned it."

Rizzo was leading the Pacific Coast League with 23 home runs, and batting .342 with 62 RBIs. He knows Jackson is eager to join him with the Cubs.

"Brett wants to be here just as bad as everyone down there [at Iowa]," Rizzo said. "Everyone is working their tail off down there, just like we hear people up here are working."

Stewart continues recovery from wrist injury

CHICAGO -- Third baseman Ian Stewart, on the disabled list with soreness in his left wrist, has been able to hit off a batting tee but that's it.

"I'm not sure if the cortisone shot gave it much relief," Stewart said Tuesday. "We'll keep taking it slow."

He received the shot last week after seeing a specialist at the Cleveland Clinic. Stewart began hitting on Saturday.

"It's still a little sore, so we're taking it slow," he said.

Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter@CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.