(CBS) The White Sox are one of three teams in the hunt for two-time Cy Young winner Tim Lincecum, MLB Network insider Jon Heyman told the Mully and Hanley Show on Monday morning.

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Lincecum remains a free agent after recovering from offseason hip surgery, and the White Sox are in the market for a fifth starter after designating John Danks for assignment. Over the weekend, White Sox general manager Rick Hahn wouldn’t confirm or deny the team’s interest in Lincecum while speaking with Inside The Clubhouse.

“From a general standpoint, we’re not going to leave any stone unturned when it comes to putting our roster in a better spot to compete going forward,” Hahn said about the White Sox’s interest in Lincecum. “Certainly, pitching depth is one of the areas the club — probably like the other 29 clubs — is going to be in the market for going forward.”

Hahn considers White Sox pitching coach Don Cooper and trainer Herm Schneider as important assets in their recruiting pitch, because both have been vital in helping pitchers revive their careers in Chicago’s south side.

Both Cooper and Schneider can be considered key pitches to Lincecum.

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“When we’re recruiting a pitcher in particular who has struggled, either with health or maximizing their performance, they know by reputation what they’re going to get by working with Don Cooper, Herm and our staff,” Hahn said. “It makes it a little easier to close those deals.”

The White Sox have the best record in the American League, entering Monday with a 24-14 mark despite a recent 2-4 road trip. They return home to face the Astros for a three-game series beginning Tuesday at U.S. Cellular Field.

Lincecum’s decision could be coming as early as Monday or Tuesday, according to Heyman. The White Sox will be eagerly waiting.

Hahn made it clear that the White Sox will do whatever it takes to win this season.

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“We have some pretty special pitching talent here in Chicago right now, and we have it under (contract) control through their primes,” Hahn said. “It would be too good of an opportunity to squander to not try to do everything in our power to put the club in a position where Chris Sale, Quintana, Rodon and others get to perform on the biggest stage in October.”