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.
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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.
