The ambitious club were only promoted last season but signed former Chelsea striker Samuel Eto’o over the summer, almost signed a deal with Manchester United over goalkeeper Victor Valdes and only recently opened their new stadium the Antalya Arena.
The Antalya Arena is a 33,000 seater stadium and the first sporting venue to be solar powered in Turkey.
Terry is out of contract at the end of the season and Chelsea are yet to renew his current deal.
The experienced defender would be offered regular football and a bumper contract at Antalyaspor. Eto’o is one of the highest paid players in the league and already has seven goals to his name this season.
Antalyaspor are currently eight in the Turkish Super League with 14 points after nine games and take on Akhisar next.