Alisson raised hopes among supporters on Thursday as he shared a photo of his gloves from the AXA Training Centre, having missed the last three games due to injury.
The Brazilian has always been slated for a return from his hamstring problem when Man United arrive at Anfield on December 17, but he could now make an earlier comeback.
“Alisson looks good,” Klopp told reporters on Friday.
“I don’t know if good enough for tomorrow, I have to check with the coaches, the medical department – and with Ali, of course.”
The manager did confirm that his No. 1 had “trained normal” on Thursday, though it seems likely that Caoimhin Kelleher will keep his place against Palace.
Mac Allister, meanwhile, is set to miss the trip to Selhurst Park having suffered a nasty cut to his knee in the 2-0 win at Sheffield United.
“Macca doesn’t look good, so we have to see day by day,” Klopp explained.
They were pretty hopeful after the game that it was not that serious – it’s not that serious, but in this period of the year, if you’re out five days it’s 12 games pretty much.
“We have to wait. I don’t expect him to be ready for tomorrow, don’t know abut Thursday [against Union SG] or Sunday [against Man United] after that.”
Joel Matip (ACL) is among the long-term absentees for Liverpool, with Diogo Jota (hamstring), Andy Robertson (shoulder), Thiago (hip) and Stefan Bajcetic (calf) also absent.
