CHICAGO -- The White Sox were ready to take the field for Sunday afternoon's season finale against the Indians, motoring to their positions one final time during the 2010 campaign.

But when the time came for the players to move out to their positions, everyone held back for captain Paul Konerko to stand alone at first base.

It could be the last game in a White Sox uniform for the heart and soul of the organization over the past 12 years, and it was going to be a memorable moment.

"Well, as I just told him today, I said, under my tenure at least, he is the classiest player that has put on a uniform," White Sox general manager Ken Williams said of Konerko, who he spoke to for five minutes in the clubhouse on Sunday. "And I'm not just talking on the field and in this clubhouse. I'm talking outside of the game as well. You'll never hear me say a disparaging word against Paul Konerko.

"We don't know how it's going to play out. There are variables at play we have to go through, to see where we are, project our revenues and how the team fits as a whole. He has some things he has to work through in his mind as well.

"If at the end of the day, even if we are the ones who choose him and he doesn't choose us, you will never hear out of anyone in the White Sox halls a disrespectful word about Paul Konerko. He is that good of a player, but also that classy of a man."

After Konerko begrudgingly took the field solo and received a standing ovation from the crowd and his White Sox teammates, catcher A.J. Pierzynski was next to the field. Eight players stand as potential free agents for the White Sox, but the tandem of Konerko and Pierzynski stand front and center -- with no disrespect to the rest.

Pierzynski and Konerko addressed their impending free agency prior to Sunday's contest, with Konerko not going nearly as in-depth as he did during a 20-minute meeting with the media on Thursday. There didn't seem to be a definitive thought about return or departure for either player, with their usual focus of the game at hand taking top billing.

Putting his own future aside during the interview session, Pierzynski joined a growing list of White Sox players in pushing for Konerko's return.

"You never know what the future holds. You never know what the market's going to be," Pierzynski said. "But at the same time, when you've had the career that Paul's had, when you look at what he's done, there should be teams lining up to get his services.

"Personally, I'd be disappointed if Paul Konerko wasn't a White Sox next year, for all he's done and for the contributions not only to the team, but to the community and everything's he's done around here. If he's not back here next year, there's something wrong. For all he's done and what he means to this team and to the people around here, it would be very disappointing."

Williams will get a 2011 budget number in late October and then another projection in November, followed by one as the team goes to the Winter Meetings and then again at the first of the year.

Ultimately, the White Sox might make the best offer to Konerko and Pierzynski within their budgetary parameters, and the players could decide to go elsewhere. Williams already had gone on record to MLB.com concerning his desire to have Konerko retire as a member of the White Sox, and he reiterated that idea on Sunday.

"Let me be clear on something: I think Jerry Reinsdorf and myself and Ozzie Guillen, we'd like to have him back. Let's be completely clear on that," Williams said. "Now, whether we can do that or that happens or not with all the variables, I have no clue right now. We are clear with our desires as we sit here today."

"I really have just no opinion on it. I'm as up in the air as any of you people are," Konerko said. "I have no feeling whether I'll be here -- or pick any team out of a hat and I would have no feeling if I could be there, either. We'll see how it develops, and once the phone starts ringing -- hopefully the phone starts ringing -- we'll see what happens."

Pierzynski also wants to come back. But the intense competitor that is the White Sox backstop for the past six years simply wants to win.

"Yeah, I want to win," Pierzynski said. "I know 2007 was one of the most miserable years ever, because coming to the park every day and knowing you didn't realistically have a chance to win and play for something was frustrating and disappointing. I haven't gotten into all the specifics of what it's going to take to go wherever, but I definitely want to be on a team that's going to compete and have a chance to win."