When asked about such a scenario by MLB.com, Williams wouldn't give a definitive response in either direction before the season even begins.
"Potentially, I don't know," Williams said. "But in terms of where we are right now, payroll-wise, there's no stress on our payroll. I wish we had a little bit more to work with, but we have to earn that."
The White Sox payroll sat at an all-in total of $127 million in 2011, which was a franchise record. It checks in around $103 million for 2012.
As for earning that extra room to work with, Williams knows his team enters 2012 with something to prove to the club's fan base.
"I said it a long time ago, you need to earn White Sox fans' patronage," Williams said. "Until we go out there and people say, 'OK,' we are not going to get the support first like some clubs and then have the ability to do whatever. It doesn't work that way."