The 29-year-old actor was seen hanging out with Bruce Willis' eldest daughter Rumer, 19, at trendy New York club The Beatrice Inn over the weekend.
A source at the club told the National Enquirer magazine: "Josh and Rumer were hanging out all night. They definitely seemed to be getting pretty cosy!"
After drinking, dancing and laughing together, the pair left the club at the same time.
He said: "You know what? I'm really attracted to British women, there's something innately proper about them. However badly they behave their accent is so cute that it makes up for everything!"
Rumer has most recently been linked to Good Charlotte star Benji Madden and British actor Ravi Gavron.