Stewart admitted to cheating on Pattinson with Snow White and the Huntsman director Rupert Sanders earlier this year, but the former couple are rumoured to be dating again.
Pattinson has apparently issued Stewart with an ultimatum, warning that he will only officially get back with her if she agrees to spend the rest of her life with him.
"Rob told Kristen the only way he can forgive her affair is if she truly commits to him. Rob has been keen to marry Kristen for quite a while and he doesn't want to get back with her unless he knows she means it for life too," a source told the Daily Star.
"Although Kristen broke Rob's heart he has realised he can't live without her. He never stopped loving her and he believes she still loves him. He is desperate to make it work and wants to give her another chance but not unless she proves she really wants it too.
"They have both talked openly about marriage before and she's been telling him for years that she doesn't want to rush into anything. But Kristen will do anything to get back with Rob now and one of the conditions is to discuss getting married and the future."
Previous reports suggested that the pair 'can't live without each other' and spent last weekend together in LA.
Watch the trailer for The Twilight Saga: Breaking Dawn - Part 2, which is released on November 12, below: