Palace are hoping to win the race to land free agent Grandin, with several other clubs in Europe trying to sign the 25-year-old.
Grandin left Blackpool earlier this summer after seeing out his contract at Bloomfield Road.
Grandin is a target for Turkish side Karabukspor and Russian outfit Krylia Sovetov, who both hope to lure him away from England.
Ian Holloway is a huge admirer of Grandin from during his time in charge of Blackpool and is keen on being reunited with the Frenchman.
Grandin flourished under Holloway during Blackpool's one season in the Premier League in 2010/11 and the Palace boss sees the wide-man as a bargain addition to his squad.