Blake Lively and Ryan Reynolds co-starred in The Green Lantern, and now they're reportedly looking to cohabitate.

The two have only been seeing each other romantically for about a month; Lively began dating Reynolds quickly after splitting from summer fling Leonardo DiCaprio.

But The New York Post says the actress, 24, and actor, 35, were spotted looking at NYC apartments together, including a three-bedroom, $4.35 million penthouse on famous Fifth Avenue in Madison Square Park.

"When they were done, she left the building first, wearing tall boots, jeans, coat and fedora, and got straight into a Town Car, and then Ryan exited into the same car," the Post's source said. "Her little dog was waiting with the driver in the front seat."

Lively lives in Chelsea -- she's in NYC most of the time to shoot Gossip Girl.