Is Jose Abreu closing in on the end of his White Sox career?

First baseman Jose Abreu has played his entire career with the White Sox, is one of their most popular players and is adored by chairman Jerry Reinsdorf.

He has enjoyed a consistently productive career, plays hurt and was the American League’s Most Valuable Player in 2020.

And he might not be back with the Sox after the third — and final — season of a $50 million contract ends Wednesday against the Twins.

‘‘Look, he’s been exemplary in terms of what you want a White Sox player to be for nine years now,’’ general manager Rick Hahn said Monday. ‘‘No matter what the future holds for him here or elsewhere, I don’t think you are ever going to hear anyone with this organization say a bad word about Jose.’’

It’s just that Abreu, probably because of his age, what he’ll cost and how many years he might want in his next deal — and perhaps because of his sagging home-run production — might be the odd man out as the front office figures out how to get less expensive first basemen Andrew Vaughn and Gavin Sheets out of the outfield.

While designated hitter makes some sense for Abreu, it also does for Vaughn and Sheets. And it has become clear that left fielder Eloy Jimenez is best suited for DH.

‘‘You find a way to do it,’’ acting manager Miguel Cairo said of keeping Abreu in the lineup. ‘‘You don’t want to lose that production.’’

Before the Sox’ 8-3 victory Tuesday against the Twins, Abreu said there had been no discussions with the front office about a new contract. Reinsdorf told Abreu he would finish his career in a Sox uniform before striking his last deal, so there’s that.

‘‘I’m just thankful and loyal to Jerry,’’ Abreu said through a translator. ‘‘He gave me the opportunity to play here, and I appreciate the opportunity. I am a White Sox. I’ll be a White Sox tomorrow. We’ll see.’’

Abreu appeared comfortable, relaxed and at peace before the game. When he talked about the fans, it felt as though it was the end for him the South Side.

‘‘I want to thank them for all the support, for always having my back,’’ said Abreu, who might have played his final game with Sox after he asked to sit out the season finale Wednesday and sit next to Cairo on the bench. ‘‘These were a special nine years, and I hope there can be more. But up to now it’s been very special, and I’m going to be forever grateful for them.’’

Abreu, who will be 36 in January, is certain he wants to keep playing.

“Claro! [Of course!]’’ he shouted in Spanish when he was asked. ‘‘I’m still hungry about the game. Once I lose that, then I know that it’s time [to retire].’’

Despite being held to 15 homers, easily a career low, Abreu hasn’t lost his hitting stroke. He hit his 40th double in the first inning Tuesday for his 183rd hit of the season, the second-most in the AL, and is batting .304/.378/.446.

His defense isn’t Gold Glove-caliber, but he also has improved that aspect of his game since his first season in the majors in 2014.

Plus, his determination never to rest and to play hurt was noted by manager Tony La Russa on his way out the door Monday. On a team wrecked by injuries, that is significant.

Abreu’s leadership was less, ‘‘We can do this,’’ as he said during the Sox’ ongoing struggle in 2022, and more about example, not unlike Derek Jeter, Cairo said.

In any event, Abreu’s contract watch will be monitored in the coming weeks.

‘‘How it fits going forward, that remains to be seen come this offseason,’’ Hahn said. ‘‘Obviously, there’s only so many different ways that you can fit various players on the roster, and Jose returning would have a ripple effect on others. But we’ll have to wait to see how things unfold and make decisions accordingly.’’