The first-choice goalkeeper has been out of action since sustaining a thigh problem against Manchester City last month, missing meetings with LASK Linz, Fulham and Sheffield United.
Caoimhin Kelleher was therefore handed rare Premier League starts against the latter two sides, shipping three to Fulham before keeping a clean sheet in a 2-0 beating of Sheffield United on Wednesday.
However, Kelleher's stint in between the sticks could be about to come to an end, as Klopp confirmed in his pre-match press conference that Alisson was training normally and could be in contention for the lunchtime trip to Selhurst Park.
"Alisson looks good, I don't know if good enough now for tomorrow. I have to check that with the coaches and the medical department, and with Ali, of course. Yesterday he trained normal," Klopp said.
On the other hand, the Liverpool boss did not have any positive news on the condition of Alexis Mac Allister, who damaged his knee during their win over the Blades in midweek.
Mac Allister required a bandage and stitches to mend an open wound, which he sustained in the first half, and he was initially able to play through the pain before having to be withdrawn early in the second period.
Klopp has conceded that the Argentine will likely be unavailable for the showdown with Palace, potentially opening the door for Ryan Gravenberch to return to the fold alongside Wataru Endo and Dominik Szoboszlai.
"Macca doesn't look good, so we have to see day by day. They were pretty hopeful after the game that it was not serious. It's not that serious but in the period of the year if you are out for five days, it's 12 games pretty much," Klopp added.
"We have to wait there how he shows up here today. I don't expect him to be ready for tomorrow, I don't know about Thursday or Sunday after that, so it's pretty much stop and go. We have to see."
Following the Reds' win at Bramall Lane, Klopp also delivered the crushing news that Joel Matip would not play again this season, having ruptured his ACL during last weekend's seven-goal thriller with Fulham.
With Matip out of contract at the end of the season, there have been fears that the Cameroonian defender may have played his last game for the club, but Klopp has hinted that he expects the club to "show their class" and offer him a new deal.
"Yeah, I'm pretty sure the club will show their class, just how you should do it. I'm pretty sure the club told Joel already that whatever happens, so as long as he is injured, everything is fine," the German said.
"And now we have to make a decision together with Joel how it looks after that. That's a normal thing to do. But, yes, he deserves all the support from us obviously and he will get it."
Liverpool are also missing Diogo Jota (muscle), Andrew Robertson (shoulder), Stefan Bajcetic (calf) and Thiago Alcantara (hip) for the lunchtime clash with Palace, where a win would temporarily take them above Arsenal to the top of the Premier League table.