The British supermodel and her actor partner were reportedly seen arguing at the Weinstein Golden Globes party in Los Angeles last Sunday.
It has been claimed the 25-year-old beauty was fuming with her tough guy after he drank too much Moët & Chandon champagne.
“Their relationship is really hanging on by a thread at the moment,” a pal divulged to RadarOnline.
“Rosie hates it when Jason acts like one of the lads and goes out drinking. She thinks his friends are a bad influence on him, and she doesn’t like it when he gets wasted.”
The Burberry model has allegedly given the 45-year-old actor an ultimatum. Rosie has warned her friends that should he continue his partying behaviour then he will lose her for good.
“When he first started dating Rosie he curtailed his wild nights out to spend time with her because he wanted to give the relationship a chance,” the source said.
“But more recently, Jason’s been having nights out with the boys and not returning home until the early hours of the morning, which infuriates Rosie. So, she put her foot down and told Jason that if he’s serious about her he has to curb his partying or she will leave him."
Rosie and Jason went public with their relationship in April 2010 after they were photographed together at the Coachella Valley Music and Arts Festival.
A year into their relationship, the couple left Britain to live together in Los Angeles.
The model's move to LA came after she landed a role in Transformers: Dark of the Moon as her acting career went from strength to strength.