(CBS) As the non-waiver trade deadline looms at 3 p.m. CT Friday, the White Sox continue to gauge the market for a hitter who can add some pop, according to 670 The Score’s Bruce Levine.

Detroit’s Yoenis Cespedes, San Diego’s Justin Upton and Cincinnati’s Jay Bruce are three outfielders on the trade block who Chicago has looked at, but the question remains. What will the cost be? At the moment, it looks to be too much.

The White Sox have no interest in parting with Tim Anderson, a shortstop at Double-A Birmingham who’s one of the top prospects in the organization. In many discussions, teams have asked for Anderson, Levine reported, but the answer’s been a resounding “no” so far.

The other factor for Chicago to consider is how another hitter would fit into the fold. The White Sox are “struggling” with how the addition of an Upton or Cespedes would affect their current unit, ESPN’s Jayson Stark reproted Friday morning, as they already have a crowded outfielder/first base/designated hitter mix. Adam Eaton is entrenched as the team’s lead-off hitter, and left fielder Melky Cabrera’s torrid hitting of late dictates that he needs to play nearly every day.

Also complicating matters is that the White Sox owe underachieving designated hitter Adam LaRoche around $13 million in 2016, so that contract looms as an albatross. It’s far from ideal to not have a spot in the lineup — this year and/or next year — for someone making that kind of money.

Cespedes is hitting .293 with 18 homers, 61 RBIs and an .829 OPS this season. He’ll be a free agent this offseason and has been linked to the Mets.

Upton’s hitting .251 with 18 homers, 56 RBIs and a .767 OPS. He will be a free agent this offseason and has been linked to the Mets and Orioles.

Bruce is hitting .257 with 17 homers, 59 RBIs and .827 OPS. He is under contract through 2016 with an option for 2017 as well. The Mets are believed to be the front-runners to land Bruce, with with the sides reportedly deep into discussions.

After a recent 7-1 road trip, the White Sox appear to have foregone the idea of being sellers. Of course, they still have a handful of holes and could use another versatile infielder as well.