The Cuban rookie is set to return Monday, and manager Robin Ventura was asked whether his struggling hitters are looking ahead to the return of the cleanup man.
''I hope they're not waiting around for that,'' Ventura said Saturday after a 4-2 loss to the San Diego Padres.
''He is coming back, but you still have to play the game. They've been good so far of just staying focused in the moment and going through it. You get a couple of days where it just doesn't look good,'' he said.
Abreu ranks among the major league leaders with 15 homers and 42 RBIs despite missing time because of tendinitis in his left ankle.
Before the game, the White Sox got a scare when Abreu was hit by a pitch just above the left elbow during a simulated game on the field and went down in pain.
Abreu got up and took about several more at-bats after receiving treatment.
''He's fine,'' Ventura said. ''He took one in the upper arm, but he's fine.''
Abreu is expected to do another simulated game on Sunday.
Minus Abreu, the White Sox have scored more than three runs in only two of their last 10 games.
Will Venable had a season-high four hits and drove in two runs to help the Padres win. San Diego improved to 20-4 this season when scoring four or more runs.
''It was a battle today,'' Ross said. ''The guys gave me a lead early. It wasn't very comfortable though. They were in striking distance the whole time. They're a good-hitting team.''
''Anytime you can find a way to get outs when you don't have your best stuff, that's what pitching's all about,'' he said.
In the third series between the two teams - and the first since 2005 - the Padres had the leadoff hitter reach base in seven of the nine innings. The White Sox managed only one runner in the final four innings.
Andre Rienzo (4-2) struggled to keep the Padres off base and consistently ran into trouble. He lasted only 3 1-3 innings, surrendering three runs on seven hits.
Twice the White Sox cut the Padres' lead to one run, but they could never pull closer.
San Diego made it 4-2 in the sixth on Alexi Amarista's sacrifice fly.
Paul Konerko's single in the second snapped his 0-for-12 stretch and put runners on the corners for the White Sox after Alexei Ramirez led off the inning with a single. A run scored when Alejandro De Aza grounded into a double play.
The Padres loaded the bases with no outs in the third. Venable hit an RBI single to center field, and Eaton threw out Carlos Quentin at the plate, keeping San Diego's lead at 3-1.
NOTES: Konerko returned to the White Sox lineup after missing the last two games because of back trouble. He went 1 for 4.