Michelle Williams Denies Romance with Ryan Gosling

05/20/2010 at 03:25 PM EDT

After getting touchy-feely in Cannes, Michelle Williams and Ryan Gosling created buzz that they could be more than just costars, prompting this response from Gosling's rep: "He is cozy with everyone!"

Now Williams's camp is setting the record straight. "They are not dating," her rep tells PEOPLE.

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The romance talk started back in January at the Sundance Film Festival where their film, Blue Valentine, premiered – they showed obvious chemistry at a cast dinner – then continued at Cannes where they held hands on red carpets.

• Reporting by JULIE JORDAN

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