This is an older movie, likely pre-1970s. A lifelong bachelor is determined to never get married, but his long time mistress wants him to propose. He doesn’t understand the point of marriage, so she decides to make him jealous by pretending to have another suitor. He eventually becomes jealous, there are some misunderstandings with him thinking more is going on with this other man than really is. In the end he decides to marry her.
Unfortunately no, though I now see that my description describes that movie too! The woman in the movie I’m thinking of is the man’s long-term girlfriend/mistress at the time of the film, and he wants to continue their relationship unmarried.