The pair were reportedly seen flirting in Los Angeles over the Oscars weekend at the Beverly Hills Hotel.
They allegedly sang show tunes together until the early hours at Crowe's suite around a grand piano.
A source said: "They were all over one another and doing little to hide their flirting. They were being really playful and jokey with one another. You could see they really hit it off. They then went back to Russell's room with some friends where they were partying until broad daylight. They were singing really loudly together around the piano, belting out some show tunes, and they looked pretty cosy when everyone left them to it."
He was previously linked to Dita Von Teese.