By Bruce Levine–

CHICAGO (CBS) — The upbeat song “Should I Stay or Should I Go” by The Clash rings out out for numerous White Sox players going into the offseason. Some on the present 25-man roster may be used to acquire talent that’s missing in the Chicago farm system and on the major league club.

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With his team carrying a losing record for the fourth straight season, ace left-hander Chris Sale said it best for all to hear Monday.

“You have to keep your head up, but something has to change,” Sale said.

The obvious names of Sale and left-hander Jose Quintana were floated throughout baseball before the non-waiver trading deadline passed on Aug. 1 as the White Sox continued to struggle, but the trades of reliever Zach Duke and catcher Dioner Navarro ended up being the only two moves that were made. Now, the White Sox have to again look forward as an important offseason looms, and here’s one of the most important questions:

If the White Sox do go into a full rebuild, will they entertain offers for 29-year-old first baseman Jose Abreu?

A strong August followed a subpar first four months of the season for Abreu, who has continued his better play into September and has 30 RBIs in the past 30 days. Abreu has hit .330 in the season’s second half after batting .272 prior to the All-Star break. With a traditional slash line of a .293 average/22 homers/86 RBIs, he’s approaching the numbers he put up in each of his first two MLB seasons, when he averaged a .298/33/104 slash line.

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Abreu is a hard-working player and sets an excellent team leader, having been nominated as a finalist for the distinguished Roberto Clemente Award, given to a player who best exemplifies a high caliber of play on the field and the charitable impact that Clemente represented in his off-the-field charity work.

From the financial perspective, Abreu can go to arbitration and void out the remaining three years on his six-year $68-million contract. With his numbers being consistent the past three seasons, it wouldn’t be a surprise to see Abreu ask for $20 million in arbitration this winter for next year’s salary.

As it sits, the White Sox have been glad to see Abreu rebound and look more like his old self after he struggled earlier in the season.

“It certainly makes you more confident as you see him over the last six weeks,” general manager Rick Hahn said. “We have an easier time projecting he will be the same player he was the first two years of his career. In candor, you certainly want him to perform to the max of what you are projecting. We have certainly seen that over the last six weeks.”

Will that be good enough to keep Abreu in a White Sox uniform the next three seasons? The White Sox have made clear they have no untouchables. Hahn will be the most popular executive — and possibly the most active in baseball — as he listens to other general managers’s offers for Abreu, Sale, Quintana and more once the season ends.

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Bruce Levine covers the Cubs and White Sox for 670 The Score and Follow him on Twitter @MLBBruceLevine.