The couple have been working together as well as dating, Us Weekly claims.
A source alleged that the duo are trying to keep their romance a "secret" but added that Dunham "has asked to use fun. songs on Girls" and is "crazy about the band".
The publication also says that the pair made a video for The New Yorker together and that Dunham wore a dress designed by Antonoff's sister on television.
Meanwhile, Dunham recently retweeted a story about Antonoff attending the MTV Video Music Awards when he was younger.
"They have a good time when they can get together," a source said.
Girls is expected to return for its new season on HBO in January.