Kanye West hasn't left Kim Kardashian's side since the birth of their baby girl, North West, on June fifteenth. But did the "Yeezus" rapper propose to the reality television star with a rare black diamond?

According the Sun, the proud parents of North West may be heading down the aisle, and it could be as soon as this September.

The Sun exclusive notes that Kanye West supposedly asked Kim Kardashian to be his bride just days after the birth of their daughter.

The Keeping Up With the Kardashians star accepted the proposal and the Sun says they're eyeing a September wedding in Paris.

There is no engagement ring at this time, but he spent £500,000 ($768,600) a gorgeous black and tiger-stripe diamond to commemorate the joyous occasion of their daughter's birth.

The 36-year-old Kanye reportedly gave Kim the diamond ring, not as an official engagement ring, but a "push present," which is a growing trend among celebrity couples not yet ready to tie the knot.

The couple is said to still be in the Cedars Sinai Hospital in Beverly Hills, California since the premature birth of North.

The Sun also reports that during their eleven day stay at the hospital, the pair has spent more than £100,000 ($153,720) on medical bills and accommodations.

The Sun sources say no expense was spared during Kim's hospital stay. The famous rapper and his reality TV star girlfriend, rented three deluxe suites costing more than £2,500 per night each.

The three-bedroom, two-bathroom suites came equipped with flat screen TVs, leather sofas, dining areas, marble bathrooms and personal chefs, who were on call 24/7.

Kim also made the use of the suite's beauty salon services, including daily blow dries, manicures and pedicures.

Not only that, but Kardashian enlisted the help of a personal labour coach at more than £3,000 ($4,600 plus) a day.

Since leaving the hospital, they've been in a secret location starting the first few days with their daughter.

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.

"He's even more in love with her now than ever and they can't wait to get married."