The Sweet Home Alabama star says he's no longer with the Frida Oscar nominee

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Salma Hayek and Josh Lucas have gone their separate ways, Lucas tells PEOPLE.

While promoting his new movie, Around the Bend, in Beverly Hills on Monday, the Arkansas-born Sweet Home Alabama actor, 33, said: “We’re not still together. I don’t really want to talk about it more than that.”

Hayek’s rep also confirms the split, saying the couple broke up three months ago.

The two started dating after the Mexican-born Hayek, 38, ended her lengthy relationship with Edward Norton.

In August 2003, PEOPLE reported, Lucas showed up on the set of a Coke commercial that Hayek was shooting in Los Angeles. The two held hands, strolled off the set during a break and eventually disappeared into the Frida Oscar nominee’s trailer.

Three nights earlier the couple popped up at a local gallery for a show of the arty furniture designed by her brother Sami.