Mr Desmond told the tribunal he had never said to anyone that he knew who Mr O'Brien would use to "get at" Mr Michael Lowry.
He denied that any such conversation took place between him and Mr Tony Boyle, chairman of the Persona consortium that came second in the mobile phone licence competition.
Mr John Coughlan SC, for the tribunal, said Mr Boyle is to tell the tribunal that he was in the box of Mr J. P. McManus at Aintree in April 1995. Mr Boyle will say he was introduced to Mr Desmond, and they discussed the pending competition for the State's second mobile phone licence, and that Mr Desmond said he "knew exactly who Mr O'Brien would use" to get to Mr Lowry.
Mr Michael McGinley, who was also in the box, would say he could recall seeing Mr Desmond and Mr Boyle talking, but was not party to the conversation, Mr Coughlan said.
Mr Desmond said he had met Mr Boyle on a number of occasions since the Aintree meeting, and Mr Boyle had never raised the alleged conversation.
Mr Boyle had not raised the issue at the time of the competition. It was now, years later, that he had first said anything about it. Mr Desmond said the conversation never took place. He said Mr Boyle had failed in his bid for the licence, and was "eaten up with envy ever since. He is a bitter man".
He told Mr Coughlan that the only reason for malice on Mr Boyle's part that he could point to was Persona's failure in the licence competition.
Mr Desmond told the tribunal he had no knowledge of the meeting between Mr O'Brien and Mr Lowry on the day of the 1995 All-Ireland final until told of it by the tribunal.
He told Mr Richard Nesbitt SC, for the Department of Transport, Energy and Communications, that he had never discussed the fact or the terms of his involvement in Esat Digifone with Mr Lowry. He had no "inside information" in relation to the licence competition.
He had made no effort to hide his involvement in the consortium. "I felt my money was as good as anybody else's. There was no exchange rate between my money and anybody else's money."
He said everything that he had learned from the tribunal over recent years had confirmed his view that the licence competition had been ring-fenced from political interference.
He told his counsel, Mr Bill Shipsey SC, that he had never had any communication "good, bad or indifferent" with Mr Lowry in relation to the licence.