"I'm not even close to dating again!" socialite Kim Kardashian says in the May issue of Cosmopolitan UK. But the reality star's words may have been printed a little too soon - as she's reportedly begun to get a little closer with rapper Kanye West.

Kim, who's in New York City to co-host the Today Show on Friday, was spotted leaving Kanye's apartment building Thursday morning after the two reportedly went to see box office smash The Hunger Games Wednesday night together - sparking rumors that the two friends are taking their relationship to the next level.

The two were then seen on a lunch date at NYC's Serafina restaurant and shopping together at various hot-spots around the city, including toy store FAO Schwarz. They appeared to keep their distance on the streets and entered shops separately, but reportedly got a bit closer once they were out of view of cameras.

Although neither Kanye, 34, or Kim, 32, have confirmed the relationship, a source told PEOPLE magazine that, "Kim and Kanye have now just started dating," but the couple are only testing the waters to "see where it goes".

But Kanye also released a new single called "Theraflu", in which he raps about his feelings for the Keeping Up With the Kardashians star - and it sounds like he's diving in head first!

"And I admit I fell in love with Kim..." he raps; "'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."

Kanye references Kim's ex-husband of 72 days, Kris Humphries, and pal Jay-Z in the song, too. Humphries plays for NBA's New Jersey Nets basketball team, which is, ironically, co-owned by rapper Jay-Z.

And Kim is reportedly planning on keeping her new relationship from being filmed and shown on any of her reality shows. A smart move, considering what happened last time.

 

See more pics of Kim from the May Cosmo UK and with Kanye in New York City on Thursday on the following pages...

 

 

 

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