The Sinn Fein Finance Minister has faced widespread calls to stand aside over the controversy, including from Ulster Unionist leader Mike Nesbitt.
But he issued a statement on Monday morning denying any knowledge of the communications between Mr McKay and the loyalist blogger.
There have been claims that Mr McKay “coached” Mr Bryson ahead of his appearance before the Nama inquiry.
“The attempts to link me to the contacts between Daithí McKay, Thomas O’Hara and Jamie Bryson are no more than petty party politicking,” said Mr Ó Muilleoir.
“They have absolutely no basis in truth or fact. I had no part in or knowledge of these inappropriate communications.
“I will co-operate readily and fully with any investigation. I am absolutely confident the outcome of any such investigation will confirm that I was totally unaware of these contacts until they were publicised this week.
“My political opponents will also have their chance to contribute to the investigation but if they do they will be required to present evidence rather than speculation or innuendo. I am confident in predicting that they will fail to do so.”