Kim's representatives have denied the reports, while Kanye's people have yet to respond to MailOnline's request for comment.
Kanye is said to have first set his sights on curvy model Leyla when he saw her dancing in the crowd at his show in Atlantic City in July last year.
And despite Kim also being present at the gig in Revel’s Ovation Hall, Kanye reportedly instructed a member of his entourage to seek out Leyla and invite her backstage.
The rapper is then reported to have invited Leyla for cocktails at AC’s HQ Nightclub, before asking her to come back to his hotel room.
However, Leyla declined, adding to the publication: 'I refused, as I felt it was too rushed.'
Kanye then reportedly asked Leyla and her friends, who had driven down from Montreal to watch his show, if they wanted to attend the concert the next evening, and gave them backstage passes.
And while Leyla admits she knew Kanye was with Kim at the time, she said the 36-year-old musician told her the relationship was 'for publicity and nothing serious'.
After agreeing to accompany Kanye back to his hotel room after chatting to him backstage, Leyla said: 'We began to make out for a while - and next thing I knew, we were both naked and having sex.'
The couple's next reported meeting came in October in New York, as Kim, who had not announced her pregnancy at that point, was in Miami.
Leyla even alleges that Kanye contacted her just last weekend to see if she wanted to meet up, but said that at that point she was fully aware of Kim's pregnancy, adding: 'I would never do that to someone.'
Follow on twitter Follow @BeautifulBlogga