Moriarty Tribunal was told yesterday. Mr Kenny was Minister for Trade and Tourism at the time.
Former FG activist Dan Egan also told the tribunal he arranged a further meeting with Richard Bruton, then Minister for Enterprise and Employment.
The purpose of the meetings was to enable Denis O'Brien to explain his interest in the second GSM licence and to outline his credentials to ministers.
Mr Egan said the meeting between Mr O'Brien and Mr Kenny in May 1995 took place at government buildings but he did not attend it.
Mr Egan also met Richard Bruton and asked him to meet Mr O'Brien, he said.
He further claimed he may have discussed Esat Digifone with Phil Hogan TD and that he may have assisted him in arranging the meeting between Mr O'Brien and Mr Kenny.
Tribunal counsel John Coughlan SC said Mr Hogan had denied any involvement in arranging any such meeting.
Mr Kenny had also told the tribunal he had no recollection of any such meeting with Mr O'Brien, although his official diary noted a meeting with Dan Egan at 5pm on May 17, 1995.
He has also informed the tribunal he had no involvement with the second GSM licence as it was under the control of Michael Lowry's Department of Transport, Energy and Communications.
Richard Bruton also denied he had any recollection of a meeting with Mr O'Brien but his diary contained an entry for Denis O'Brien at 7:30pm on May 17, 1995.
He agreed he was a member of the Cabinet committee that decided how to proceed with the tender competition for the licence but he had no further involvement with it.
Mr Egan also informed the tribunal Mr O'Brien had engaged him to develop his profile with the Fine Gael party.
He advised Mr O'Brien to attend FG fund-raising events.
Subsequently, the Esat Digifone chief attended a golf classic on May 29, 1995, where he contributed £4,000 to the party.
At another fund-raising event in the Glenview Hotel during the Wicklow by-election that year attended by Michael Lowry he presented a cheque for £5,000.
In June of the same year he presented a further cheque for £1,000.