"We don't know yet," Cooper said. "It's still to be determined and won't be until the last few days, I would guess."
"That will be the last call we make," Guillen added. "We have a couple of guys out there we're looking at, and it's not going to be an easy one."
Relief jobs already belong to closer Bobby Jenks, Octavio Dotel, Scott Linebrink, Matt Thornton and left-handed specialist Boone Logan. Mike MacDougal has all but locked down the sixth spot with four straight scoreless outings, leaving two prime candidates and a bit of an outside shot for No. 7.
The opening could be filled based on how far the starters are stretched out during Cactus League action and the team's confidence in these five working deep into games. Nick Masset would be more of a long-relief candidate, having made three starts this spring, while Ehren Wasserman, who burst onto the scene with the White Sox at the end of the 2007 campaign, would be a one-batter or one-inning type of pitcher.
Wasserman, who threw one scoreless inning Sunday against Arizona, held right-handers to a .174 average last season but left-handers batted .533 (8-for-15). With that flaw in mind, the sidearm-throwing right-hander has made a few spring adjustments.
Although he's only thrown the pitch a couple of times during games, Wasserman worked on improving his changeup. He's also worked on a few different variations of his already unique arm angle and moved from the third-base to first-base side of the mound when facing left-handed hitters.
"I've also worked on my fastball command, pretty much almost everything," said Wasserman with a smile. He has produced a 3.68 ERA over seven spring games, after posting a 2.74 ERA in 33 games last year. "It has been progressing positively, and hopefully, it will translate over to the season."
D.J. Carrasco, a veteran non-roster invite who has pitched parts of three previous seasons for the Royals, has worked his way into contention for a roster spot, with two more scoreless innings against the Cubs on Saturday giving him his second save and lowering his ERA to 1.29. But Carrasco appears to be more of a strong choice in reserve, one the White Sox can turn to at Triple-A Charlotte if Major League struggles occur.
Until Wasserman arrived last year, the team lacked those solid relief options from within. Now it has more than a few viable choices to fill out the staff.
"I guess I have three or four more outings," Wasserman said. "I just have to get people out and make it tough on them. If I go to Charlotte or whatever, I'll just continue to work, try to get better and do what I can to get back."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.