The couple are said to have browsed around a West Hollywood boutique after deciding that getting married is the "logical next step" in their relationship.
"[Kristen] loves Rob, and she's finally ready - and engagement is a logical next step," an alleged friend told Metro.
"In the past year, they've really heated up - moving in together, travelling together, introducing each other to friends."
The rumours come after Pattinson and Stewart attended the wedding of a top Hollywood producer in New Jersey two weeks ago.
Onlookers at the celebration said that the Cosmopolis actor stuck to Stewart's "side all night".
The pair are also believed to be writing a script together.
Photo gallery - The Twilight Saga: Breaking Dawn - Part 2:
Copyright: Lionsgate/Summit Entertainment