Actor Penn Badgley's relationship with X-Men: First Class star Zoe Kravitz is heating up - the couple has moved in together.

The former Gossip Girl hunk has been dating rocker Lenny Kravitz's daughter since late 2011 and they recently took their romance to the next level by renting a loft in Williamsburg, New York.

Badgley conducted an interview with New York Magazine at the couple's home and gave journalist Carl Swanson a tour of the brick-walled pad, which features a red sofa, a large box of records, multiple guitars, a ukulele, framed portraits of Jimi Hendrix, a jar of model airplanes and a digital projector for movie nights.

He says, "Look at where I live. I mean, all of my friends live very much the way I do except for the fact that they have no money, you know what I mean? We all hang out, we do the same things, we all live in a similar way, and I happen to have this massive, beautiful apartment."