The Australian actress, who is best known for her roles in Triangle and Mullholland Drive, has been married to 46-year-old film director Claudio Dabed for 11 years but they have not been seen together since March.
George has been spotted with hip-hop star Russell Simmons on various occasions over the past two months, according to the Sunday Herald Sun. They were reportedly seen kissing at a New Jersey football match on Wednesday and also attended a New York film premiere together.
George and Dabed met in Bali in 1998 and married two years later. She has previously spoken of her good relationship with his teenage daughter Martina.
In 2009, George said that she was considering having a baby with her husband and a year later, she admitted that her parents were "disappointed" that she had not become pregnant yet.
In February this year, she said that she finds her job "hard" because it involves being away from Dabed so often and she "misses" him.
Simmons, who founded Def Jam and is believed to be worth $340 million (£207 million), used to be married to reality television star Kimora Lee Simmons.
Watch Melissa George in the trailer for Triangle below: