The DUP leader said he was told he would be welcome in the UUP.
Sir Jeffrey Donaldson has denied that he had any plans to rejoin the Ulster Unionist Party after he was defeated in a DUP leadership battle last year.
However, the current DUP leader has said that he was told he would be welcome in the UUP, but “respectfully declined”.
Sir Jeffrey was defeated for the DUP leadership by Edwin Poots in May of last year.
However, Mr Poots was forced out of the role within weeks following an internal party revolt, and Sir Jeffrey later became leader.
The BBC Nolan Show said Sir Jeffrey had discussions with UUP leader Doug Beattie, before he became leader.
In a tweet, the DUP leader said he was approached by the BBC and asked if he had discussions about leaving the DUP and joining the UUP, of which he is a former member.
He said: “I never had any such intentions or plans.
“At the time, I was approached, and it was made clear I would be welcome in the UUP but I respectfully declined.
“Any discussions I had with the UUP focused on the future of unionism and the need for closer unionist cooperation.”
TUV leader Jim Allister told the Nolan Show: “I think there are many unanswered questions including was there a face to face meeting, what was discussed and who initiated these matters.
“If it were to turn out that Sir Jeffrey contemplated rejoining the Ulster Unionist Party then that would be a very big shock to many rank and file DUP members.
“If you join a party, you show loyalty to the party and the leader and you expect that to be reciprocated.
“If there was contemplation of leaving that party then that would cause great discomfort among the rank and file supporters.”