The TV host's denials come in response to a Monday report from NW which declared the two were sharing an apartment in Bondi, Sydney after Mel allegedly offered Rhyce a place to stay in her garage.
Mel clarified the living situation in a statement to Daily Mail Australia, glibly saying: "I can confirm that I don't have a garage that I store a stash of men in."
She added Rhyce had attended a couple of group dinners at her home but assured the publication that was the extent of their relationship.
The 36-year-old later took to Instagram to share her amusement at the story, sharing a video of Daily Mail's article with the caption: "Some articles are just too ridiculous that you just need to laugh.
"Apparently not only is @heather_maltman bunking with me even though she has a radio show on the Gold Coast, old mate @rhyce_power is living in my garage.
"If anyone needs a place to stay there are currently 6 spots available in my garage for $100pn, you can just pop your little blankie in the corner and pee in the bucket."
The sensational claims gathered pace when Perth-born Rhyce told his social media followers he was relocating to the east coast and asked fans for help finding somewhere to live in the "Harbour City".
Further quashing speculation of a romance with Mel, hours ago the tatted up hunk shared a selfie with his rumoured girlfriend Vanessa Sierra before they jetted off to Thailand together for a three-month health and fitness retreat.