The 26-year-old actor was left devastated when his "Twilight" co-star publically admitted this summer that she had cheated on him with her "Snow White and the Huntsman" director Rupert Sanders.
Pattinson is said to be desperate to get back with the brunette beauty but he wants full commitment from her, reported Daily Star online.
"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 said.
"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," the source added.
Pattinson, whose "Twilight" character Edward Cullen marries Stewart's alter-ego Bella Swan in the film franchise - had plans to pop the question to the actress shortly before she broke the news about her infidelity.
While she has previously not wanted to rush into marriage, the 22-year-old star is said to be ready to do anything to win Pattinson back.
"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. Rob is very romantic and traditional," a source said.