"Kim and Kanye have now just started dating," a source told People, adding that they are keeping things "light" but are open to seeing "where it goes."
The pair have been friends for years, with West, 34, even making appearances on Kardashian's reality show on E! Rumors have long swirled that there was more than friendship between them.
Kanye didn't help matters with his new song "Theraflu," in which he sings, "I admit I fell in love with Kim … 'Round the same time she fell in love with him … That's cool, babygirl, do your thing … Lucky I ain't had Jay drop him from the team."
West is referring to Kris Humphries, the reality star's estranged husband, who plays for the New Jersey Nets, owned by West's pal Jay-Z.
Kardashian is still fighting to end her 72-day marriage to Humphries.
But, it appears she has moved on. The nascent couple were spotted leaving a showing of "The Hunger Games" Wednesday and lunching at Serafina in New York City Thursday. Earlier, Thursday morning, Kardashian was photographed leaving West's apartment wearing the same black leather pants and white and gray sleeveless T-shirt she was sporting the previous evening.