Hammer told host Jimmy Fallon that he is only linked to the Batman role through rumors and that he hasn't had any conversations with Warner Bros.
"This is the thing about rumors. They're all fine, they're all well and good, but none of the people who start rumors are actually the people who can give you jobs," Hammer said before stating that he is open to becoming the caped crusader.
"Who wouldn't want to be Batman?" he said. "It's a good gig."
The role of Batman is open after previous star Ben Affleck stepped down from the part in January.
Hammer appeared in the film, based on the novel of the same name by Andre Aciman, alongside Timothee Chalamet. Luca Guadagnino directed.
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"Who knows? I mean, like, here's the deal. Andre Aciman wants to write another book. Luca wants to write the script," he said.
"Timmy and I are down as long as they give us each $12 million," Hammer joked.
Aciman and his publisher Farrar, Straus and Giroux confirmed on Wednesday that a second novel titled Find Me is on the way.
"The world of 'Call Me by Your Name' never left me. Though I created the characters and was the author of their lives, what I never expected was that they'd end up teaching me things about intimacy and about love that I didn't quite think I knew until I'd put them down on paper," the author said in a statement to Vulture.
"The film made me realize that I wanted to be back with them and watch them over the years -- which is why I wrote Find Me."
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