The 23-year-old beauty is said to be missing pet pooches Bear and Bernie "like mad" since she split with Robert for a second time three weeks ago, and wants them to split them up and have one each.
A source told the Daily Star newspaper: "Kristen thinks they should have one each.
"She's missing the dogs like mad, but doesn't want the situation to turn nasty."
The 'Twilight' hunk - who went on a date with Katy Perry last week - was recently spotted with both dogs in his pick-up truck after moving his items out of Kristen's house.
The pair only moved back in with each other in March when Robert returned from Australia - where he was shooting 'The Rover' - and he was said to be looking forward to spending some quality time with Kirsten and their pets.
A source previously said: "The first person he wanted to see and spend time with is Kristen, and of course Bear and Bernie."
Robert dumped Kristen for a second time after she got back in touch with 'Snow White and the Huntsman' director Rupert Sanders, who she confessed to having an affair with last year behind his back.