Bradley Cooper and Renée Zellweger on a Date?

Bradley Cooper and Renée Zellweger on a Date?
Renée Zellweger and Bradley Cooper
Jackson Lee/Splash News Online

07/01/2009 AT 12:55 PM EDT

That Bradley Cooper certainly gets around. Last weekend he was in Paris, where he fended off rumors about a possible relationship with Jennifer Aniston after they were seen together in New York.

Then, Tuesday night on Manhattan's Upper East Side, the Hangover star, 34, was seen with Renée Zellweger, 40, at the Italian restaurant Antonucci.

"She didn't really eat much, but he ate," someone in the restaurant told PEOPLE, adding that the two looked like they were on a date. "They were very flirty. Either he's being very gentlemanly, 'cause that's the way he is, or they're dating. He paid. He pulled out her chair, that kind of stuff."

As for their time together, "She had a coughing fit at one point and got up and left, but then came right back," said the source.

Zellweger's rep has no comment. But a source close to the Cold Mountain Oscar winner says, "They did New in Town together and they stayed friends. That's it." And, a source close to Aniston tells PEOPLE, "She and Bradley are still talking."

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