The Indians have Travis Hafner under contract through 2012 as the team's designated hitter, with a combination of Victor Martinez and Ryan Garko at first base. But Thome was so embedded in the community and as a part of the organization during his run in Cleveland from 1991-2002 that the chance for him to come back could be intriguing.
As far as Thome is concerned, those sorts of issues can wait until the season is over to thoroughly explore.
"My main focus is to stay healthy and look into now," Thome told MLB.com prior to his scheduled day off on Wednesday. "The bottom line is Cleveland was very special, as have been all the cities I've played.
"Philadelphia was great, and I wouldn't have changed my experience there for the world. Chicago has been tremendous, being able to come back home.
"In this business, you never say never," Thome said. "But focus on the task in front of you. Don't get ahead of yourself and try not to get into 'Is this going to happen?' or 'Is that going to happen?' For me, I try to enjoy every minute of the latter part of my career here."
Following his highly productive stint with the Indians, during which Thome had seven seasons of at least 30 home runs, he signed a six-year, $85 million deal with the Phillies as a free agent. Thome was traded to the White Sox prior to the 2006 season and has not exactly received a warm reception in his yearly returns to Progressive Field.
It's not something that Thome takes personally, not when he continues to hit as he does at the Indians' home ballpark. He has a .300 average, seven home runs and 25 RBIs in 26 games played there as an opponent.
"Coming back is always nice," Thome said. "It's always fun hitting in this park. When I step in the box, it's a good feel.
"This is the issue. Fans are very passionate, and you have to understand as a player, whenever you leave a place where you spent a long time, where fans love you and show passion to you, you have to understand when you leave, there's potentially a negative reaction. They have the right to boo.
"I understand that. You move ahead," Thome said. "You don't regret any decisions, because when you make decisions you have to live by them."
With Thome still a viable option as a hitter, and an even better option as a quality clubhouse presence, there figures to be teams interested in bringing him into their future fold. For now, Thome is a proud member of the White Sox and that's the only point of interest for the 38-year-old potential Hall of Famer.
"You do wonder, you definitely wonder, obviously I want to keep playing," Thome said. "If something would happen where I couldn't return [to Chicago], I have to look out there and say which team would I want to play for. I try not to go there.
"I've had such a great time in Chicago, and I'm so blessed I was able to come back and be a part of this great organization. But out of respect to all parties, you just play baseball. You try as you get older, don't get ahead of yourself. You look what's out there, but you don't disrespect anybody."