The Pirates of the Caribbean and Star Trek Into Darkness actress has been spotted out and about with Marco Perego, an Italian artist who was once nicknamed Pirate Perego thanks to his Johnny Depp-like long hair and goatee, the New York Post's Page Six reports.
"They're hanging out for sure, but it's very new. It's nothing serious yet," a source close to Saldana tells PEOPLE.
One source told the Post, "They looked very close and were later seen kissing" at the Star Trek afterparty. But the report quotes another source, who said, "Zoe and Marco have known each other for a while as friends. It's too early to say they are dating."
A rep for Saldana would not comment on her personal life.
Perego, 34, was once a promising soccer player in Venice, but came to New York a decade ago after a leg injury ended his career. Within five years he was a rising star in the art world.
Saldana, also 34, split from her fiancé of 11 years, entrepreneur Keith Britton, in 2011. After that, she had a yearlong romance with Bradley Cooper.
In the June issue of Allure, Saldana says she is done dating actors. "Been there, done that, got the T-shirt," she says.
She also raises the possibility that she might eventually "end up with a woman raising my children ... that's how androgynous I am!"