The Scottish veteran was the first ever actor to portray the suave British secret agent in 1962's Dr No, and went on to play James Bond seven times.
The series is set to return to the big screen with Daniel Craig slipping on his tuxedo for his third outing as the spy next year (12) to coincide with the 50th anniversary of the franchise.
Bosses at MGM - the studio behind the movies - are planning to mark the milestone with a special event in which all former Bonds talk about their dealings with the character.
According to Britain's News of the World, Pierce Brosnan, Timothy Dalton, George Lazenby and Roger Moore are all in talks to be part of the celebrations, but Connery has snubbed the opportunity.
A source tells the publication, "Not having Sean would be a sad thing for these celebrations. We hope he will change his mind."