Konerko is at the end of a five-year, $60 million deal he signed after the White Sox won the World Series.
The organization seems to want him back, but everything depends on the budget that will be set for the 2011 season. The White Sox already have about $75 million guaranteed for next year and several arbitration-eligible players.
"There's no doubt in anybody's mind they want him to be back here," manager Ozzie Guillen said of his bosses, Kenny Williams and Jerry Reinsdorf.
"Money-wise, that's another problem. Do we want it? We all do, there's no doubt.
Hopefully they get something done. We'll see what happens."
Konerko hasn't campaigned for a return or really spoken to reporters too much about his future. Konerko, 34, has had a whopper of a walk year, hitting .310 with 38 homers and 107 RBIs, so production isn't an issue. He's also still very able at first base.
"I think where they stand right now is probably just figuring out where they want to go as a team. I'm kind of secondary," he said. "That goes for the other guys here who are in the same boat. Obviously it's a business, so they have to figure out payroll stuff and when they do that, then hopefully I'm in their conversation, as far as being brought back. Until then, I don't know what will happen."
Konerko said he will have to examine several factors before making a decision on where to play, hinting that it won't be a snap to re-sign here if the opportunity arises.
"It's about the game," he said. "It's not so much about the contract or the years or the money. It could be that I get more here and don't come back. You know, I got a family to think about. How do I fit on a team? There are a lot of things that go into it. I've made a lot of money in this game and it's not all about that. At the same time when it gets to those situations, it's always been that the player has to take the discount, never the team going above to get him back. You see it from all angles."
Konerko's reputation has only grown in the organization since 2005, and he said he's finally comfortable in the role as clubhouse leader. He's the second-best power hitter in White Sox history, behind Frank Thomas, and is closing in on 400 home runs (364 before Thursday's game).
"He's the leader of the team and we need him back for that purpose alone,"
Gordon Beckham said. "If he does what he did this year next year, great. But he's the leader of the team, and I'm not sure if he leaves this team, if there's anyone here who can fill his shoes right off the bat. We need him mentally as much as we did physically on the field."
Konerko said he wants to win another World Series and he thinks the White Sox have a winning situation in place. But he said they can't keep the status quo to catch the Minnesota Twins, who easily won the AL Central. He noted that the organization needs to "tidy up" things on and off the field.
"Strictly speaking from the talent and the guys, I believe it's a team that can fight and win," he said. "I mean I do think that things need to get better. The Twins are a good team, a great team, and more than that they go about it the right way. You have to go out and catch them. They're not going to come back to you."
Jon Greenberg is a columnist for ESPNChicago.com.