"They're trying to keep it a secret," explains a Dunham pal. And the NYC-based actress/writer, 26 -- who has described her love life as a string of "multiple gay ex-boyfriends" -- is already collaborating with Antonoff, 28.
The pair recently made a video for The New Yorker together, and Dunham "has asked to use Fun. songs on Girls," notes a source. "Lena's crazy about the band," says a pal. She also wore a dress designed by his sister, Rachel, on The Colbert Report May 3.
Despite hectic schedules, says an insider, "they have a good time when they can get together!"
Fun.'s hit song "We Are Young" was No. 1 on Billboard's Hot 100 charts for six consecutive weeks in March and April. Their follow-up "Some Nights" has spent 27 weeks on the Hot 100 chart. The group is nominated for two awards at Thursday's 2012 Video Music Awards. Antonoff shared a photo with MTV on Monday of his favorite memory of attending the 1997 VMAs as a young child.
"I was in that age where it was very cool to ask everyone for pictures," he explained. "I go up to Fiona Apple, and this is like 10 minutes before she gives her iconic speech. I ask her for a picture, and right as the camera snaps, she gives me this wet, like almost a little bit of tongue and full-lip kiss on the cheek."
Dunham tweeted the cute story and pic Monday, writing, "Best thing that's happened yet in America."