The two, who were first revealed to be dating in early April, have both put their homes on the market, according to TMZ.
They are reportedly hoping to sell their houses in preparation for renting a home together.
Kardashian is said to be asking for $5 million (£3.25m) for her home.
Earlier this month, it was reported that the couple are already thinking about marriage.
Kardashian has yet to finalise her divorce from basketball player Kris Humphries, who she wed in August of last year.