The 17-year-old reality TV star, who started dating the 25-year-old rapper in October following his split from ex-fiancé Blac Chyna, believes she has found ''The One'' and hopes he will get down on bended knee in the near future.
A source close to the 'Keeping Up with the Kardashians' star said: ''To say she's obsessed with him would be an understatement. He can do no wrong in her eyes. She's dying for him to propose - she drops hints about it all the time. If he suggested they elope together, she would do it in a second.''
But the teenager's family, including mother Kris Jenner, have urged her to slow down and enjoy her youth before she decides to settle down.
The insider told US OK! magazine: ''For the first time in their lives they're speechless.''
Another source previously admitted Kris and ex-husband Bruce Jenner are concerned about their youngest daughter's relationship, saying: ''Her parents know she is going to date who she wants, but they are worried he will have a negative impact on her decision-making.
''A lot of Tyga's friends are enablers. That makes her mom the most nervous. She doesn't want Kylie getting off track.''