A lawyer for Arlene Foster has threatened legal action against doctor and TV presenter Christian Jessen.
Dr Jessen is one of a number of people who have tweeted an unsubstantiated rumour about the DUP leader's private life.
Through her lawyer, Paul Tweed, Mrs Foster has emphatically rejected the allegation as false.
Mr Tweed said, if necessary, legal proceedings would be taken against Dr Jessen.
In a statement issued to BBC News NI, Mr Tweed said: "I would confirm, if necessary, legal proceedings will be taken against Dr Christian Jessen, Twitter and any persons who have recklessly retweeted this false and highly defamatory allegation".
Mrs Foster is a member of the Northern Ireland Assembly for Fermanagh and South Tyrone and served as first minister of Northern Ireland from 2016 to 2017.
Dr Jessen is best known for presenting Channel Four programme Embarrassing Bodies.