He's Just Not That Into You
actress was initially delighted when a trio of the furry critters began approaching her in her backyard, but is now worried they are taking over.
A source told the National Enquirer magazine: "At first three or four squirrels visited Drew when she went outside for a cigarette break - she called them Luke, Fab and Spike after a trio of her ex-boyfriends. But now more than a dozen flock to her each day."
The 34-year-old star fears she will struggle to get rid of the pests, who are used to her feeding them nuts and tortillas.
Drew is not the only star to be plagued by animals.
It was recently reported Kate Moss was being "driven mad" by a flock of doves flying into her London home.
A source said at the time: "They've started relieving themselves over her antique furniture leaving unsightly stains and a vile smell.
"Kate has spent hours running around the place trying to make them fly away. Unfortunately, the doves seem to have taken a real shine to her."