The pair are said to be planning a September wedding in Paris, reports the New York Daily News and The Sun.
While West is said to have asked Kardashian, 31, to marry him without an engagement ring, reportedly spent upwards of $500,000 on a rare black diamond ring as a gift to mark the birth of their child.
Kardashian gave birth to her first child Saturday 15 June, a month ahead of her scheduled due date.
Kardashian had taken out a birthing suite at Cedars-Sinai Medical Center in Beverly Hills, Calif., a world-famous hospital of choice among many celebrities including Britney Spears, Victoria Beckham and Jessica Simpson.
The reality star reportedly shelled out in access of $100,000 on her four day stay at the hospital.
A source told The Sun; ‘Kanye wasted no money in making sure Kim had the best of everything while she’s in hospital. He has spent half a million on a ring as a push present and had it designed months ago in preparation,” according to The Sun. He’s even more in love with her now than ever and they can’t wait to get married.’
Kim only finialized her divorce from her second husband Kris Humphries earlier this month after a long and bitter legal battle.
Their marriage lasted just 72 before Kim filed for divorce in October 2011.
Kim was also married to music producer Damon Thomas from 2000 until 2004.