The couple - who married in 2012 and have children North, four, Saint, two, and Chicago, three months, together - are said to be in talks with major film studios about having their love story told on the big screen, and they're willing to show the highs and the lows of their romance if they receive the right offer for the project.
A source said: ''Kim and Kanye have had no shortage of offers to make a biopic.
''But they were either for low-budget productions or bigger studios dropping hints that never materialised.
''But now the likes of Warner Bros. and Sony are wooing them, so they figure a movie could be a huge hit if it's done right.
''The key is not to make it cheesy and highlight the positive aspects of their relationship. But they also know they can't sugarcoat the fact they've had problems.''
However, one thing putting potential producers off the project is the level of creative control the couple want on the film.
The source told heat magazine: ''Kanye wants his music to play a central part. He loves singing to Kim and the kids and seeing them in the audience at his concerts.
''Whoever plays him will have to be very talented in that regard.
''Kim is mainly concerned about issues such as surgery and how her family will be portrayed.
''She knows there's a need for certain dramas to be included but she and Kanye are insisting on a lot of control over the script, which is why it will take some time before it's formalised.
''But they're keen to make it happen this year.''
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