Basketball player Humphries, 27 — who is locked in a bitter divorce battle with Kim — made the allegations in text messages to former girlfriend Myla Sinanaj, according to US gossip website TMZ.
Humphries was linked to Myla after he and Kim, 31, split last October 72 days after their wedding.
The texts have come to light as part of divorce proceedings, after Kim's legal team asked for them to be surrendered as evidence.
|Sex tape ... Kim Kardashian|
Humphries has been fighting to have the marriage annulled, saying that the split left him heartbroken and that Kim duped him into the wedding.
Other texts are claimed to reveal that Humphries told Myla he was in love with her — and wanted to get his divorce from Kim out of the way quickly.
Sources close to Kim, who is now dating rapper Kanye West, are said to have claimed that she never even discussed the tape with Humphries.
Kim shot to fame in 2007 when the raunchy sex tape featuring her and her ex-boyfriend, singer Ray J, was released on the internet.
Speaking about the tape to US TV host Oprah Winfrey earlier this week, Kim's mum Kris told how the X-rated clip was "humiliating" for the family.
She went on: "No mother ever wants to hear something like that. I could tell she was in a lot of pain."
Kim also spoke to Oprah about the tape, saying: "You know, I think that's how I was definitely introduced to the world.
"It was a negative way, so I felt like I really had to work ten times harder to get people to see the real me."