(CBS) While sporting a lower profile than some of their foes making noise in free agency, the White Sox remain in the market for a veteran right-handed starter and are still considering the big names, CBSSports.com MLB insider Jon Heyman reported Thursday morning.

The White Sox still have their eye on “even the top guys — Max Scherzer, James Shields and Ervin Santana, plus trade possibilities such as Jeff Samardzija and others,” Heyman reported, adding that Chicago has had “contact” “with the biggest pitchers.”

Of those, Scherzer seems like quite the long shot, given than “several big-spending teams are expected to get into that long-developing derby,” according to Heyman. The White Sox continue to express interest in trading for Samardzija, a northwest Indiana native who has one year left on his contract but hasn’t given any indication that he’s ready to sign an extension before hitting the open market.

What Chicago has going for it, though, is some payroll flexibility, and that keeps it in the mix. Prior to free agency starting, the White Sox had a little more than $60 million committed for 2015. Since then, they’ve signed first baseman/designated hitter Adam LaRoche to a two-year, $25-million deal and left-handed reliever Zach Duke to a three-year, $15-million deal.

Chicago’s payroll of $91 million in the 2014 season was the 22nd highest in baseball, according to spotrac.com.

With left-handers Chris Sale, Jose Quintana and John Danks in the rotation — and young lefty Carlos Rodon with the chance to win a spot for next season — it’s been no secret that the White Sox covet a right-handed starter.