The King of Staten Island star also revealed he has been inundated with ticket requests for SNL after it was revealed Taylor Swift will be the next musical guest - but he won't help anyone.
He quipped: "Yeah, nobody is leaving me alone about it. I just tell everybody that like... they don't give me tickets."
It was previously claimed Pete and 41-year-old Kim - who has children North, 8, Saint, 5, Chicago, 3, and 2-year-old Psalm with Kanye - are "a little more" than friends.
A source said: "Kim and Pete like each other. They are trying to play it off that they are just friends, but it's a little more than that right now. They're having a lot of fun together.
"Pete makes Kim laugh and makes her feel special. Pete is obviously thrilled and has a major crush on Kim."
Kim and Pete - who split from Phoebe Dynevor in August - have both recently emerged from high-profile romances, and they've been bonding over their experiences.
A second source said: "Kim and Pete spent time together in Staten Island at one of his favourite spots, Campania restaurant.
"Pete and Kim have been enjoying their time together and are having fun. Both are recently single and have bonded over that."