But Abreu's providing more anyway.
For the third time in less than a week, Abreu has voiced his unwavering intent to be a part of the White Sox for the foreseeable future, even though his current contract is up at the end of this season and he's slated to hit the free-agent market.
Speaking Tuesday from the American League clubhouse at the All-Star Game, Abreu laid it all out there once more, just like he did a day prior, giddy over what the White Sox are building on the South Side and the thought of being a part of it.
"That tells you how good we are right now and how good we can be," he said through team interpreter Billy Russo, asked what it meant to have teammates joining him at the Midsummer Classic after being the lone White Sox representative a year ago. "And we're going to be very, very good.
"That's why I'm telling you guys that if the White Sox don't sign me, I'm going to sign here anyway. I'm going to sign myself here. I'm going to be here, believe me. I'm going to be here.
"I don't want to miss this, I don't want to miss what is coming, and I'm going to be here."
It's an obvious example of how much he enjoys being a part of this organization, despite the fact that he's never played for a White Sox team that finished the season with a winning record. As he's been tasked with - and willingly adopted - the role of acting as a mentor to guys like Yoan Moncada and Eloy Jimenez, who are expected to be the stars of future championship teams, he's had a front-row seat to all the talent Rick Hahn's front office has acquired since starting this rebuilding process.
He knows what's coming.
After blasting a walk-off home run in a picture-perfect day for the rebuild - the same day Dylan Cease won in his major league debut - he said he saw the White Sox building "something very big" and that "I don't want to leave here."
Monday, during All-Star media responsibilities in Cleveland, he said: "I think my desire to stay with this team is getting bigger every day, after every game. We are good, and we're going to be very, very good. For me, there's no secret. I want to be here."
So, yeah, it's been pretty darn obvious what Abreu's ideal outcome is: staying in a White Sox uniform. And he's going to do it himself if he has to.
That doesn't sound like it will be necessary, though. The White Sox have raved about him as much as he's raved about them, and it's been no secret that they would like him to be a part of their future, too.
"We, obviously, are biased," general manager Rick Hahn said last week. "We get the benefit of seeing what he does in the clubhouse. He is a modest and humble producer year in and year out and a great asset to us, both on the field and off.
"He helps teach (young players) professionalism and helps teach them commitment and day-in, day-out commitment to trying to win a championship. He is relentless in his pursuit of making himself the best, and he takes those young guys under his wing and sort of shows them the path.
"I don't think he takes for granted a single day in the big leagues and takes an extreme amount of pride in wearing a White Sox uniform, and he models that for the young players in this organization."
Hahn went on to call Abreu a model player, and after hearing what his All-Star teammates, Lucas Giolito and James McCann, said Monday about his impact, it's almost impossible to envision the good times coming for this franchise and Abreu not being a part of them.
It almost seems like the White Sox feel about Abreu the same way they've felt about players who now have their numbers retired and have statues in the outfield at Guaranteed Rate Field.
Abreu might be providing more evidence than is necessary about how he'd like things to shake out. But the feeling appears to be mutual.