Kanye West did not pop the question to Kim Kardashian soon after the delivery of their daughter North West, a source close to Kardashian told People, quashing speculation that the reality TV star is engaged to the rapper.

On Sunday, British tabloid The Sun came out with a report saying that Kardashian had accepted West's proposal and that the couple would tie the knot this September in Paris.

Although West did not give her an engagement ring, The Sun said, the rapper presented Kardashian with a push present -- a gift that a new father gives the mother of his child -- in the form of a “rare black and tiger-stripe diamond ring.”

A source close to Kardashian dismissed the news, but stopped short of denying the possibility of a wedding. "I can't imagine them not getting married," the source told People. "That's in their future!"

Rumors of a wedding have been doing the rounds ever since Kardashian announced her pregnancy in December, and various reports indicated that West was all set to propose marriage soon after the baby was born.

West is apparently keen on marrying Kardashian, as he sees a long future with her, and wants to have many more children with the reality show personality, according to British magazine Now Daily.

The magazine stated in a February report that West has set his eyes on having five more children with Kardashian.

"Kanye grew up as an only child and the Kardashians have been a revelation to him," according to a Now Daily report. "He wants his kid to have loads of siblings, so he's told Kim not to get cosy with just one baby. He'd like them to keep making babies until they have at least six."