According to reports from Nice Matin and Foot Mercato, Crystal Palace have submitted an offer of €50 million for the highly rated 22-year-old.
Monaco have turned the offer down, however, and are holding out for a massive €60 million to part ways with one of their most prized assets.
Camara is under contract with the Ligue 1 side until the summer of 2029, so Monaco aren’t under any immediate pressure to sell.
New manager Felipe Luis is hopeful he will be with the club beyond the summer transfer window.
Speaking after the 3-2 pre-season win over Liverpool, Luis said: "Yes, of course I have hope. I have every hope that he stays. I think he is happy at Monaco.
“If he stays, he can work even harder. Because he will play, as I said, a key role in my system."
Fellow Premier League sides Liverpool and Man United have also been linked with a move for Camara.