The Eagles were linked with a move for the 26-year-old Germany-born forward in the summer but failed to push through a deal for him.
However, the Londoners' need for a new striker has intensified after a disastrous start to the new season as Christian Benteke has picked up a long-term knee injury to leave boss Roy Hodgson short of quality in that area of the pitch.
Hodgson will be given funds to spend in January and he could cash-in on some of his current players to try and bolster the squad and ensure that Palace avoid relegation, following their seven-game losing start to the season in which they have failed to score a goal.
There has been talk of a £22.4million bid for Tosun, who helped fire Besiktas to the Turkish title with 20 league goals last term, with Orman quoted as saying that he will instruct coach Senol Gunes to sell if a deal will benefit the club.
He told Haberturk: "If the proposals are very serious numbers and we need to sell to benefit the club, we will sell. But your opinion is also important. If the proposals arrive in January, we will sit back and talk."