"I had a real good conversation with Kevin when we informed him we were declining the option the other day," Hahn said on "The Waddle & Silvy Show" on ESPN 1000. "This is the first time Kevin has had a chance to be out on the open market, and he's got a young family out on the West Coast, and he wants to explore what's out there.
"But he knows there is no confusion in his mind about our desire to bring him back. So we're going to stay on that, stay in communication. It's not a great time to be a club in the free-agent market looking for a third baseman, the player pool is not real deep, so I expect Kevin will be popular, but we're going to be in on that until the end, I think."
Youkilis batted .236 with 15 home runs, 46 RBIs and 47 runs scored in 80 games with the White Sox last season. He was acquired June 24 from the Boston Red Sox along with cash considerations in exchange for infielder/outfielder Brent Lillibridge and right-handed pitcher Zach Stewart.
Hahn also said there's a chance, though probably not as great, that A.J. Pierzynski will return.
"There's absolutely a chance," Hahn said. "Given the history and level of communication, there's certainly a chance until he's elsewhere. We had A.J. for eight years, which I think is a lot longer than people expected.
"He's been fantastic for us, just like Mark Buehrle was. ... Unfortunately we had to watch Mark walk out of the door, because it was the best thing for Mark and the best thing for the organization given his market at the time. That could well happen again.
"But we signed A.J. for eight years. We had three multiyear deals in the mix, and we've got a good relationship with him and his agent, so at least each side is going to make a decision with their eyes wide open. If this is the end, it was a great run. If not, hopefully we can continue it."
Pierzynski is coming off his best year, hitting .278 with 27 home runs and 77 RBIs.