The Oscar-winning actress and the James Bond star are believed to have got together on the set of upcoming thriller Dream House, while speculation about their status intensified at Christmas after they were spotted on a "romantic" countryside break.
The Daily Mail now reports that the pair were "all over" each other while celebrating Weisz's 41st birthday at a Hollywood restaurant this week.
Onlookers at the establishment also claim that the suspected couple were discussing plans to purchase a home in New York.
Craig and Weisz both split with their respective partners, producer Satsuki Mitchell and Black Swan director Darren Aronofsky, last year.
