Gardner spent last season on loan at Selhurst Park and is now a free agent following the expiry of his contract at Hull.
Palace have been trying to secure the former Tottenham centre-half on a full-time deal, but are facing competition from rival Championship clubs.
However, Eagles assistant manager Lennie Lawrence says the club are not giving up hope of having Gardner in their squad next season.
Lawrence told the Croydon Advertiser: "We are still trying to re-sign Anthony Gardner.
"I think he wants to stay, but as is always the case there are other clubs interested. Hopefully we can bring that one to a satisfactory conclusion though."
Source: Team Talk
Source: Team Talk