The pair were first rumoured to be dating in early April and finally went public with their romance last week at Scott Disick's New York City restaurant opening.
According to US Weekly, Kardashian and West are serious about their relationship and have discussed making a long-term commitment.
"[They] are talking marriage," a source told the publication. "She wants to be with him as much as possible. They really know and love each other."
The insider also claimed that Kardashian will join West when he is on tour with Jay-Z this summer.
It was recently reported that Jay-Z's wife Beyoncé disapproves of West dating Kardashian.
> Kanye West meets Kim Kardashian's family