The 82-year-old legendary actor - who has made very few public appearances in recent years - is said to have been lined up for a James Bond tribute at the 85th Oscars ceremony.
Daniel Craig, Sir Roger Moore, Timothy Dalton, George Lazenby and Pierce Brosnan are also set to take to the stage at the same time, reports the Daily Record.
The James Bond franchise will be receiving a special tribute during the ceremony to mark its 50th anniversary.
A source stated: "Sir Sean has been invited to take to the stage along with Daniel and the other 007s. As yet, we've not had a no from him. Normally he is quick to turn things down.
"Sean's relationship with the Oscars is good and we're hoping he'll appear."
Connery has turned down other opportunities to take part in Bond celebrations in the past - including a 50th anniversary documentary - due to a dispute with movie bosses over pay.
The insider added: "His issues with the Bond producers are not our business and we hope he will overlook that as we pay tribute to what he has done.
"It would be magnificent to see him up there with the other actors – and quite a coup.
"We're very close to getting Adele to talk to us about a performance too. Until she is officially nominated this week for the best film song Oscar, we can't invite her."
Nominations for the 85th Academy Awards will be announced on Thursday, January 10 at 5.30am PT (1.30pm GMT).
The ceremony will take place at the Dolby Theatre in Los Angeles on February 24.
James Bond: 50 years of 007 - pictures: