The teen star wants to make a movie about Moss and star in it herself - to show people she can really act.
A friend of Olsen says, "Mary-Kate absolutely adores Kate Moss.
"She was so worried about her when she went into rehab (for cocaine use) and she even wrote her really nice letter offering her support and friendship."
The 19-year-old believes the two have a lot in common and are both "independent, free spirits".
The source adds, "Mary-Kate think that she would be able to bring the right edginess and depth to the role.
"She sees Kate as a survivor, just as she is herself."