The couple are said to be giving each other some space in order to repair their relationship following "lots of arguments".
"There is no other person involved," an insider told the MailOnline.
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"They love each other very much and are not making an announcement because they're still hoping to work things out.
"But things have not been good. There have been lots of arguments and they both need some space. They are taking some time out from each other. Bear in mind there's an almost 20 year age gap between them – they are going to run into some issues."
Model Rosie, 26, recently opened up about her relationship with Hollywood actor Jason, 45, in an interview with Elle magazine for the October issue.
"Many models are in long term relationships for stability," she said. "Admittedly, not always with great men, but it gives them something to come home to, something grounding.
"That's how I see my relationship. Well, I see it in many ways but one of the most beautiful things is that I feel at home wherever I am in the world because of him."
She also denied that their age gap was ever an issue in another interview. "I'm not interested in hanging out with boys," she said. "I have all the man I need. His knowledge and strength are really inspiring and attractive, and that can come with a man who's had a bit of time.
"We have a connection that has nothing to do with age. Work comes and goes, but if you have someone at home who thinks you're the greatest person in the world, that keeps you going."
The Marks & Sparks beauty has been dating The Expendables star since 2010.
She is currently holidaying in Ibiza with some girlfriend. She arrived on the island on Sunday and has been sharing her holiday snaps on Twitter.