Sakho joined Palace on loan for the rest of the season in the closing stages of the January transfer window, ending a miserable six months on Merseyside.
The Frenchman had been exiled by Klopp due to a dispute in the summer, instead training and playing for the Liverpool U23s for the first half of 2016/17.
And when asked whether Sakho had a future at Anfield, after his spell away, Klopp urged the 26-year-old to “concentrate on Palace.”
“First of all, if I should give advice to Mamadou Sakho it would be to him, not for TV,” he told reporters on Thursday afternoon.
“Who knows in half a year, we felt already what can change in a month, now there’s five months left.
“He should concentrate on Palace, we should concentrate on here.
“At the moment he’s on loan, still has a contract at Liverpool, but it’s not a thing we talk about in this moment.
“That was a solution [for January], then we can wait for a new impression. But that’s nothing I think about in this moment.”
Sakho has already got stuck in with training under Sam Allardyce in Croydon, and could come into contention for Saturday’s relegation six-pointer at home to Sunderland.
It would seem that the France international has already taken Klopp’s advice, as he explained on his move to Palace.
“The most important thing is for us to win a lot of games,” he explained.
“I know we have a good squad, I have a few friends who are playing here. They called me tonight, like [Christian] Benteke. For me the objective is to win.
“I feel happy, I have trained with the second team at Liverpool and have my own fitness coach to do extra work.
“I am happy to come here, it’s a challenge which is really exciting. Right now it’s a new page for me.”
It seems unlikely that Sakho would return to Klopp’s squad for 2017/18, particularly given Liverpool’s willingness to seal a permanent deal for the defender.