The Strokes drummer Fabrizio Moretti says the 'Charlie's Angels' actress has lost her ample bosom through dieting and he is determined to get them back to size.
However, Drew is apparently furious with her musician boyfriend because she fears the extra calories will ruin her figure.
A source is quoted by Britain's Daily Mirror newspaper as saying: "Drew loves her figure and gets angry when Fab tries to force fatty foods down her." Drew recently insisted she will never feel under pressure to become a Hollywood waif and will always be proud of her curves.
She said: "I'm never going to fall prey to that. I don't have enough room in my life for the neurosis of other people's expectations. If you're too thin, they kill you and if you're too fat, they kill you.
"There's no such thing as perfection and someone else's definition of it is not good enough for me.
"I love food too much to live in fear or starvation. If I could eat macaroni cheese every day then I'd be happy. I live for crispy tacos!"