The actor joked about a rumor Cooper was his "new lover" after they were photographed at the French Open
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Bradley Cooper and Alessandro Nivola might just have the ultimate bromance.

The Tony-nominated pals and costars of Broadway’s The Elephant Man hit up the French Open last weekend to take in some tennis – and some of Nivola’s friends gave him some grief about it.

“He’s got this apartment in Paris, which is just incredible, and we went down and had front-row seats to watch Roger Federer, who’s his buddy. And there we were just watching tennis, and a couple days later, I’m told by some friends that Bradley is now my new lover,” Nivola, 42, told PEOPLE at the 69th Annual Tony Awards on Sunday.

While he’s been happily married to actress wife Emily Mortimer since 2003, Nivola quips, “If I were gay, he’d be the guy, I’m tellin’ ya.” (Most recently, Cooper’s been linked to model Irina Shayk.)

The actor had nothing but good things to say about Cooper, 40.

“He’s the greatest actor to be on stage with because it’s just different every night,” says Nivola, 42. “We’ve done the show 115 times, and every night, it’s different, and that’s because he’s just so super free, and we play off of each other that way, and we’re determined not to let it get boring and stale and dead, and it’s thanks to his commitment that way – his talent.”

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And Nivola isn’t the only costar smitten with Cooper: Patricia Clarkson wasn’t shy about to heap on the praise.

“Oh, [Bradley]’s very sexy. And so is Alessandro Nivola – they’re the sexiest men alive, oh my god,” says the actress, 55, who was also up for a Tony Sunday night.

As it turns out, Nivola also spends time with Clarkson offstage.

“I just have such close relationships with both of them, in different ways. Patty got me into So You Think You Can Dance,” adds Nivola. “She’s obsessed, and now I’m obsessed, too. We used to sit together and drink bourbon and watch So You Think You Can Dance.”