The star couple - who are still in love - are said to be on a trial separation as they seek to repair their relationship following ''lots of arguments''.
The pair will apparently not release an official statement because they remain relatively optimistic they can move past their problems by giving each other ''some space''.
A source told the Mail Online: ''There is no other person involved. They love each other very much and are not making an announcement because they're still hoping to working 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.''
The 26-year-old model and actress has recently denied the age difference with Jason, 45, was a problem, and she even commented on their ''stability'' in an interview to be printed in the October issue of Elle magazine.
She said: ''Many models are in long term relationships for stability. 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 of the most beautiful things is that I feel at home wherever I am in the world because of him.
''You've got someone special to go back to when the s**t hits the fan.''
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