The pair met 8 months ago, very soon after Khloe divorced her husband Lamar Odom.
"The relationship got too heavy and Khloé needed to take a step back", a source told American magazine Us Weekly, with another adding that French was "needy".
"It grated on her that he became so dependent on her," the insider told the magazine.
French played a big role in Khloé's life this year, helping her to celebrate her 30th birthday and hanging out with the extended Kardashian family.
However Khloé flamed the rumours this week by posting an inspirational quote on her Instagram page.
"Maybe one day we'll find that place where you and I could be together. And we'll catch our dreams within the waves of change," she wrote.
"So smile for me one last time and believe that we'll meet again. Until then, I'll be missing you."