The 36-year-old rapper asked the reality star to marry him just days after the couple welcomed their first child, The Sun reports.
The pair are said to be planning a September wedding in Paris.
A spokesperson for Kim was unavailable for comment on Sunday.
Kim gave birth to her first child Saturday 15 June - a month ahead of her due date.
Mail Online exclusively revealed that the reality star had been admitted to hospital in Beverly Hills the night before.
The reality star is said to have splashed out more than $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??Mbuta Nanga'' on a ring as a push present and had it designed months ago in preparation.'
TUMESHIRIKI KUTOKA DM. Mimi nasubiria HARUSI TUUUU"