The TOWIE star, 25, is said to have met the troubled brother of Kim on a night out in Las Vegas where the pair hit it off.
According to The Mirror, the pair swapped numbers and are planning to meet again soon.
In fact, the newspaper reports that the pair met as long as two years ago, when Ferne was still dating former TOWIE star Charlie Sim.
And while they aren't thought to have seen each other since, they have apparently kept in touch on Whatsapp and email.
Now a source claims that 28-year-old Rob is planning to visit the UK later this year and hopes to meet up with Ferne.
The source says: "Rob likes Ferne because she is more down-to-earth than the girls he is used to in LA and he finds her easy to talk to."
When asked about Rob, Ferne admitted that the pair have been messaging each other.
She told the newspaper: "I have got plans to go to LA, but only because I've wanted to go for ages."
Could there be a budding romance in the air? We hope so!
While Ferne split from long-term love Charlie last year, Rob has previously dated X Factor judge Rita Ora and Cheetah Girl Adrienne Ballon.
Rob is unusually reclusive compared to his other family members, and likes to keep out of the spotlight.
Last month, reports claimed Rob is planning a return to reality show Keeping Up With The Kardashians after losing 15 pounds gave him a big confidence boost.
Kim's sibling made headlines around the world when he flew home from Kim's wedding celebrations in Paris in 2014, before her actual marriage took place.
And there was the time Rob shocked fans when he shared an image of fictional Gone Girl killer Amy Dunne to Instagram, saying it reminded him of Kim...
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