The Sun says Chamakh is wanted on a six-month loan as the Eagles bid to beef up their attack.
Chamakh looked to be heading back to France this summer with his old club Bordeaux.
But Palace have stepped in after pulling the plug on a deal for free agent Carlton Cole.
An Eagles insider said: "Chamakh's now top of the manager's wish-list.
"He wants a targetman to compliment Dwight Gayle and Chamakh fits the bill. Holloway feels he can bring the best out of him and has always rated him.
"The plan is to bring him in for six months and see how the move works out. By that time Glenn Murray should be back fit and in contention."