The 22-year-old model, who is friends with the 'Keeping Up with the Kardashians' star's younger half-sister, Kendall Jenner, reportedly regrets giving her number to the 27-year-old sock designer.
A source said: ''He's been bombarding her with text messages, and it's creeping her out.
''She's not attracted to him at all and is pretty insulted that he would think he had a chance.''
Meanwhile, Rob, who has rarely been seen out in public over the past year as he has been struggling with depression after gaining more than 50 pounds, is said to be in ''really bad shape'' at the moment and is struggling to cope with news his step-father Bruce Jenner is transitioning into a woman.
The source told America's Star magazine: ''He's still in a downward spiral. He's so lonely and desperately wants to find the right woman, but his confidence is at rock bottom. He really wanted Cara to like him.''
Rob has been struggling to get his life back on track since splitting from Cara's close friend Rita Ora almost three years ago.
The former couple were inseparable during the summer of 2012 but he accused her of cheating on him ''with nearly 20 dudes'' after they split that December.
The Chats' debut album High Risk Behaviour is the most punk thing we've heard in years.
Nature-inspired songs we just can't get enough of.
Put these British films about music at the top of your watch list.
How has coronavirus affected the music world this week?
James Righton's latest album is well-produced, well-arranged and put together very proficiently and professionally.