The former footballer was allegedly seen arriving with the lingerie tycoon at her home in London after a party at around 2.30am, before eventually leaving at around 6am, according to The Sun.
The pair had earlier attended the Pride of Britain Awards at London's Grosvenor House Hotel on Monday.
A source had claimed: "They went in together and I saw them at the window of the first-floor flat before Michelle closed the front room curtains.
"Minutes later the lights went out."
However, Savage has denied the tabloid allegations, tweeting: "Can't believe the rubbish they write in the papers sometimes!!!"
Mone also dismissed any claims that they were in the property on their own, stating: "I was not alone in the flat with Robbie.
"I am friends with Robbie and his PA Trisha, who lives in Nottingham and was staying with me that night."
She added: "Robbie is a good guy and my friend — but just not my type."
Robbie's spokesman Paul Mace said: "He spent a very enjoyable evening at the awards.
"He walked back with Michelle to meet up with his PA who was at Michelle's apartment.
"He stayed less than an hour before catching a taxi to his hotel."
Michelle Mone announced her separation from husband Michael back in December after 19 years.