The Sporting Lisbon forward has been in fine form in Portugal this season.
The Eagles are thought to be searching for a new striker in the January transfer window, with them severely lacking in that area of the team this season.
Alan Pardew’s side have been tracking several strikers ahead of this window, and Slimani is thought to be chief among them, with them having scouted him on several occasions already.
They have already had a big rejected for the Algerian, with website Le Buteur claiming that they had had an offer of £15milllion rejected by the Portuguese side.
That has not deterred them though, and instead they may offer as much as £22milion for the striker, which would activate a release clause currently in his contract, according to A Bola.
£22million would certainly be a big price to pay for the Algerian, although this goalscoring record this season is vastly superior to what Palace currently have to offer.
He has managed 12 goals in 15 appearances in the league so far for the Portuguese side, with him currently second in the top goal scorers charts.
That leaves him far ahead of Palace’s current crop, with Connor Wickham currently their only striker to have scored in the Premier League this season.