Leyla Ghobadi, 24, told Star magazine she had sex with West after he picked her out of the audience at one of his concerts in Atlantic City last July.
Ghobadi said Kardashian, who is now pregnant with West's first child, was also at the show, cheering West on from a VIP section and oblivious to the fact he was hitting on another woman nearby.
"This is going to destroy the Kardashian family," Ghobadi told Star. "It's bad. It's really bad. It's just embarrassing. But if I were Kim and about to have a baby, I would want to know."
Ghobadi went on to say she was initially concerned West was dating Kardashian but he assured her the relationship was "for publicity and nothing serious."
Ghobadi said she also slept with West in October in New York while his reality TV star girlfriend was in Miami.
Ghobadi alleges West tried to get her to have sex with him again as recently as this past weekend, but she turned him down because Kardashian is just weeks away from delivering her baby.
"I would never do that to someone," Ghobadi told Star.
The New York Post said Kardashian's representative has denied there is any truth to the tabloid report and West's publicist didn't respond to its request for comment on the story.