But Milner has since not returned to full training, and it is now unclear whether he will be passed fit to feature against the Eagles.
Speaking ahead of the trip to south London, Klopp told reporters Milner was suffering from illness, and would need to be assessed on Friday afternoon.
“A few knocks, how it always is. Nothing else,” he said when asked about injuries.
“Milly was ill on Tuesday, so he had no chance [against Spurs].
“Yesterday he had a running session, to see how he felt. It was OK. So he’s had two days, but I’m not sure. Apart from a few knocks, we’re OK.”
Milner’s absence could see Alberto Moreno continue at left-back against Palace, and the Spaniard was in strong form at Anfield on Tuesday.
Moreno has impressed Klopp in training sessions since his demotion to second choice in August, and will relish the chance to make his first league start since the opening day of the season.
With Milner the only major doubt, Klopp has diverse squad to choose from against the Eagles.
His major selection quandary comes in midfield, with Jordan Henderson returning after missing the victory over Spurs through suspension.
Furthermore, in attack, Daniel Sturridge‘s brace in midweek could see the No. 15 keep his place in the starting lineup, but Sadio Mane, Philippe Coutinho and Roberto Firmino are also primed to feature.