Abreu looking more and more like a keeper for White Sox

He's traded four veteran players since July 13, and Chicago White Sox general manager Rick Hahn is open to making more deals in advance of Monday's 3 p.m. nonwaiver deadline.

If the right offer comes along, Sox first baseman Jose Abreu could be the next one to go.

But more likely than not, the 30-year-old Abreu is staying put. For two reasons.

First, Abreu still has a potent bat that can help the Sox win some games during the rebuild.

Well, maybe not win, so we'll defer to Rick Renteria.

"We're trying to keep our games, beyond trying to win them, at times we're just trying to keep them respectable," the White Sox's manager said. "We don't like games to get out of hand."

So, there's that.

Second, there is also value in leadership, which is going to be needed as more and more young players reach the South Side.

Abreu has already been a positive influence on fellow Cuban Yoan Moncada, the No. 1 prospect who joined the Sox last Wednesday.

It's a role Abreu would like to expand.

"Even though my English is not good, I've been trying to communicate with the young guys and with everybody," Abreu said through interpreter Billy Russo. "They were asking me to be more vocal to try to help them, to try to speak with them in certain situations, to give them advice. And I've been trying my best.

"I think that's something good, not just for them but for me to do more. I don't want to say be a leader, but like a mentor for them because I have some experience and I think that my knowledge can help them to do better, too."

Renteria is impressed with how Abreu has come through some difficult off-field issues. Last year, he reunited with his son for the first time in three years after defecting from Cuba.

In March, Abreu told a federal jury how he ate a part of his fake passport to cover up an illegal smuggling operation in 2013.

"I think he is in a better place," Renteria said. "I think he's more comfortable in his own skin and everything that's been going on. Obviously, he's had some things go on in his life but I think he's dealt with them quite admirably.

"I think he's going out on a daily basis doing the best he possibly can and continue to do what he's got to do in between the lines. He's able to compartmentalize and separate things outside of the field."