While the 38-year-old actress has said in the past that she does not want to wed, Gosling believes he can convince her otherwise, reported Contactmusic.
"Ryan is head over heels in love with Eva and he wants to have a life with her, including children. It's something Eva has baulked at in the past but Ryan has a charming way of helping her see a different kind of future. She's getting on board with the idea of marriage," a source said.
The actor has been dating Mendes since May.