Wallace took to social media on Monday to respond to the claims, posting two Instagram stories.
In the first one, he said the story “was investigated promptly when it happened six years ago by the BBC and the outcome of that was that I hadn’t said anything sexual.
“Do I need to repeat this again? I didn’t say anything sexual. Thank you for your time.”
He then posted a second story, in which he said: “Nobody six years ago accused me of flirting with anybody or hitting on anybody.
“The reason I say this is because of my wife Anna. I have always been true to my wife Anna.”
He added that he had “never flirted or hit on anybody” in the twelve years that he has been with his wife.
“It’s important that, so that people don’t misunderstand that, that I am true to my wife.”
Wallace is best known for co-presenting cooking show MasterChef.
The allegations come at a difficult time for the BBC. Earlier this year, the corporation’s former most senior news presenter, Huw Edwards, received a suspended jail sentence after pleading guilty to child sex abuse image offences.
In August, Jermaine Jenas, who presented The One Show and appeared on Match of the Day for the BBC, was sacked by the corporation following complaints about workplace conduct.
A BBC spokesperson said: “Whilst we do not comment on individuals, if issues are raised they are dealt with swiftly and appropriately at the time. We do not tolerate any form of inappropriate behaviour and have robust processes in place.”
You can contact BBC News by emailing: haveyoursay@bbc.co.uk, external