Trainer Herm Schneider said Konerko made considerable progress in his recovery from a bone bruise near his left knee, two days after he was hit by a pitch. The captain, though, isn't expected to start swinging a bat again until Wednesday afternoon.
"Because (Wednesday) he's going to start hitting to see how it feels -- it's going to be hard for him to say, 'I'm good, let's go play,'" Guillen said. "I said I know we need you but in the meanwhile I don't want him to go out there and start getting bad at-bats just to be there."
Adam Dunn was back at first base Tuesday in the Yankees' 6-0 rain-shortened victory, one night after a couple of misplays at first in the first inning Monday led to a pair of runs in the Yankees' 3-2 victory.
Guillen said that when Konerko does return, he will do so at first base and not ease back in there by getting a few games at the designated hitter spot.
"We're better obviously when PK's at first base," Guillen said. "I think we need good defense. He's not the type of guy that's going to move out there all over the place, but I think if you're looking for him, he'll be at first base. If he can't tolerate that much pain for three or four hours then I will change my mind."
Konerko is batting .305 with 25 homers and 76 RBIs for the White Sox, who are in third place in the AL Central.
While Konerko was unable to go, Yankees' shortstop Derek Jeter returned to the lineup after missing Monday night's series opener with a bruised middle right finger. He'd also been hit with a pitch Sunday against the Orioles.
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000.