Peavy was to begin "tossing," not throwing, in early January, Williams said during a break at the Major League Baseball General Manager Meetings.
"I am preparing in my mind that this will be something that we take very slow and we're very careful with so that we can make sure we get a solid healthy season out of him and not have him less than full strength and less than all he can be," Williams said. "I'm not looking at April, in my mind, but he may surprise me."
Despite the injury, Williams said the White Sox head into 2011 with pitching depth. The rotation should include Mark Buehrle, Gavin Floyd, John Danks, Edwin Jackson and Chris Sale, who has begun an offseason training program designed to increase his stamina for a potential starter's spot.
In his first big league action last season, the 21-year-old went 2-1 with four saves and a 1.93 ERA in 21 appearances. He allowed five runs on 15 hits and 10 walks, while striking out an impressive 32 batters in 23 1/3 innings after being called up in August.
The White Sox drafted Sale 13th overall in the 2010 First-Year Player Draft with the intentions of getting him into the rotation at some point.
This past spring at Florida Gulf Coast University, Sale went 11-0 with a 2.01 ERA in 17 games. He struck out 146 and walked only 14 over 103 innings.
Asked if he expected to acquire another starter, Williams said the team has six now and would add another depending "on how much we want to shake it up."
Williams said Brent Morel is the leading candidate to be the White Sox starting third baseman. As for Dayan Viciedo, Williams said there's no denying the infielder will be an impact player.
"Whether his time will be now or later will be dependent on what's available in the free-agent market," Williams said.
"We've got good pitching, and that's a [heck] of a place to start. However, we've got to do a better job of catching the ball for them. Too many balls are put in play that have not turned into outs and that's one of the things we want to address."
As for White Sox free agents Paul Konerko and A.J. Pierzynski, Williams said he's not sure how the offseason will play out and whether the two will return.
"First of all, I respect them tremendously," Williams said. "Guys like A.J. Pierzynski, he's a catcher who comes to play every single day and they're not easy to find. Guys like Konerko are leaders and class individuals who produce in the clutch, and they're not easy to find or easy to replace.
"By the same token ... we've had to say goodbye to some players. I'm not afraid to do that. To a large, large degree, it's not even in my control. It's in their control, to a larger degree. Now, one could say, 'If you stepped up with the money, then you take your lion share of the trophy.' I don't know if that's the case in this scenario. You're talking about people who money is not the end-all. They factor in the totality of their life."
Williams described his conversations with other general managers and agents during this week's meetings at the Waldorf-Astoria Hotel as very different from years past.
"To a large degree, I'm more in a listening mode than I've ever been in coming to these meetings," he said, "because I have to wait and see what's available to us, what's available via free agency and what's available via trade and then put it together and say, 'This gives us the best chance to win in 2011 and win beyond that.' Right now, there is no defined path."
Williams said the White Sox plan will evolve, although he cautioned that the team may have the exact same players after December's Winter Meetings as it does now.
"For fantasy purposes, dreaming purposes, I could put together one [heck] of a team right now," he said. "In reality, actuality, you can't rush the calendar."