CLEVELAND — Increasingly over the course of a four-game series at Guaranteed Rate Field last month, the visiting Yankees found themselves talking in their dugout about White Sox slugger Jose Abreu.

Abreu wore out the AL East heavyweights, collecting 10 hits in 17 at-bats as the Sox earned a split.

“I mean, he killed us,” said Yankees veteran pitcher CC Sabathia, who took a loss in that series, giving up a single and a double to Abreu and getting chased during the fifth inning. “We were all talking about how tough a hitter he is, how hard to face he is. He’s one of the best hitters in the game. His swing is short, quick, powerful. He barrels everything up. Man, I’m telling you — his swing is going to play forever.”

Wouldn’t forever be nice?

And wouldn’t a while longer — even just another few years — be nice for the rising Sox and their ready-to-win fans?

“I don’t know why [the Sox] wouldn’t want to keep him,” Sabathia said. “He can still play first base. He can hit. And the bottom line is he’s a championship player. He’s a player who can lead the clubhouse — not just the Latin players.”

Abreu, 32, was as clear during All-Star festivities as he has been throughout the season: The free-agent-to-be wants to stay with the Sox beyond his sixth season with the team.

A three-time All-Star, Abreu has 21 homers and 66 RBI. The latter figure is one off the AL lead.

“Nothing has changed in terms of our view of Jose and his value to this club and how he potentially fits going forward,” general manager Rick Hahn said. “We tend to handle these things in the offseason, so it’s a little premature to worry too much about it right now. But it’s good to hear that he feels as strongly about us as we do about him.”

Abreu smiled as he described the scene last week on the South Side when his three-run, 12th-inning walk-off homer gave the Sox a doubleheader sweep of the Tigers. Abreu took off his helmet and kissed it as he neared home plate after reaching out and yanking a Nick Ramirez breaking ball into the bullpen in left. A mob scene with teammates left him on his knees — talk about smiling.

It was the best he had felt in a Sox uniform in a long while.

“The difference was we have a good team. We have a team with good guys, guys with good hearts, guys who like to work hard,” Abreu said through translator Billy Russo. “That moment was special because I think it showed people that we can do good things, that we’re working for good things — that we’re going to be good.

“That’s the way I can summarize that moment, all the happiness, because we are going to be good and people will start seeing what we can do. . . . I really believe in this team. We have a good team, with good kids, and I’m just very, very happy to be with this team right now.”

Sox All-Star Lucas Giolito called Abreu an “amazing bridge” between what could be on the field and what is right now with the team’s promising young core.

“I owe this to my parents,” Abreu said. “They taught me how to be thankful, and I am very thankful to the White Sox because they gave me the chance to play at this level. They gave me the chance to make my mom’s dreams come true.”

And about that earlier word: “forever.”

“I want to be with [the Sox] forever,” he said, “because I’m really thankful with all the things they have done for us, and especially for me.”