The 38-year-old comedian fuelled dating rumours after he was pictured walking arm in arm with Khan on recent outings, reported Daily Star.
The socialite is reportedly finding Brand's growing affection as obsessiveness.
"Jemima's started to get a bit freaked out by Russell's relentless affection. She's described him as compulsive and obsessive," a source said.
"It's like he's addicted to her. She likes him but it's still too much," the source added.
Brand, who was previously married to pop star Katy Perry, first met Khan two years ago when he wrote an article for her magazine.
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