Minaj, 26, branded suggestions that she and the Umbrella singer were living together “insane”.
“I don’t know where people got this really insane, hilarious, random rumour that she and I were living together,” she told a US radio show.
“We had just shot the video for a song I have on the album called Fly. When I saw her the first thing I said was ‘So, did you hear we’re living together’.
“We just started cracking up laughing and she was like ‘I can’t believe people are this ridiculous’.”
But the Pink Friday singer confessed that she has not ruled out the possibility of hooking up with Rihanna, 22.
“We’re not getting cosy. I mean, we’re not getting cosy yet,” she laughed.
“There is a possibility because she’s just like a bad a**. You never know. That would be like a crazy power couple right now.”
Rumours began to circulate about Minaj and Rihanna being more than just good friends on internet forums earlier this month.
The pals, who duet on the song Fly, fuelled the gossip even further by posting a string of suggestive messages on their Twitter accounts.