"He hit in St. Louis [on Saturday] and had some discomfort, and also his hand felt weak," Piniella said Wednesday. "He's backed off. He'll probably be ready, I would think the second series after the break."
That would be the Cubs' series at Arizona, July 21-23.
The Cubs have notified Major League Baseball that Soriano will not be able to play in what will be his seventh All-Star Game.
"[Soriano] is going to the game, but he's not going to be able to play," Piniella said.
When he was informed that Soriano would be unable to play, National League manager Clint Hurdle said that he would need to wait and see how the situation developed before selecting a replacement.
"I will do the selection if and when we get to that point," Hurdle said. "But I have to hear from [Major League Baseball senior vice president] Katy [Feeney] first, from the National League office."
If a selection needs to be made, Hurdle will be able to choose which player fills the final spot on his roster. He said that he would want to wait to select a replacement until after the Final Vote results are announced at 5 p.m. ET on Thursday.
"There's a lot you can do," Hurdle said. "But you have to let [the fans] finish the vote, then you'll see where you are. Without a doubt, I think that would be appropriate to wait."
Soriano suffered a broken bone in his left hand when he was hit by a pitch by Atlanta's Jeff Bennett, and took batting practice on Saturday for the first time since the incident. The Cubs would like Soriano to consider a Minor League rehab assignment when he gets closer to being ready.
"We're going to approach him on it," Piniella said. "I think it would be good for him. This hasn't been a two-week thing, it's going on five weeks or so, and that's a long time. You need to get your legs under you a little bit, catch some balls, have him play one game under the lights. We'll see. I think it would help."
Meanwhile, left-handed reliever Scott Eyre, who has been on the DL since June 27 with a strained left groin, will throw Thursday and Saturday for Class A Peoria. The Peoria Chiefs have Friday off, which is why Eyre can't go on back to back days. Eyre will not be activated until after the All-Star break, Piniella said.