Liverpool are prepared to offload Mamadou Sakho on a permanent basis if a club were to table a bid of at least £30m ($39m) for him, reports say.
Sakho, 27, played eight games for Palace after making his debut for the club against Middlesbrough in February.
He helped the Eagles stave off relegation to the Championship but picked up a knee injury against Tottenham last month and is unlikely to feature against Manchester United on 21 May.
The Guardian says Palace are interested in making Sakho's move to Selhurst Park permanent, but are assessing whether they can afford to sign him.
There is also no certainty that Sakho will agree to a permanent move to Palace, with Paris Saint-Germain reported to be interested in bringing the defender back to the French capital.
Palace chairman Steve Parish said Sakho's performances had been pivotal in helping the club avoid relegation and confirmed that he would try to make the Frenchman's move to Selhurst Park permanent.
"You can't con anyone that he didn't make a massive difference," he was reported as saying.
"We won some massive games with him. He's a really nice person, a big character, he's got the respect of all the players, and it's one we'd like to do. But, of course, we have a lot of things we need to do in the summer, and the money needs to work for us and for Liverpool.
"I'm sure there'll be a negotiation on that. If we can make it work, of course we'd like to, I'm not going to try and be coy or clever on that.
"He's a very good player and I think he likes being with us. We like him. Let's hope we can do it."
In an interview in April, Sakho said he had not given up hope of playing for Liverpool again.
"I still have three years on my Liverpool contract. If I have to wear the Liverpool shirt again, I'll do so with pleasure. If I have to wear another shirt ... we'll see," he told Telefoot.