The 'Charlie's Angels' star was reported to have ended her four-and-a-half year relationship with The Strokes drummer, but his friends say it was him who did the dumping.
A source told The National Enquirer: "Fabrizio got tired of waiting for Drew to decide about marriage.
"She wasn't sure if she wanted to have kids. She has been making a documentary about her troubled family and has been haunted by a family history plagued with mental illness and addiction ever since she started the project.
"She was scared her children might inherit some of the problems.
"Fabrizio has been her rock for years but he finally had enough." Drew, 31, and Fabrizio, 26, previously split in 2005 but were soon reconciled.
The Strokes drummer was recently seen on a date with 'Spiderman' actress Kirsten Dunst.