The Dublin government gave an apparent seal of approval to the SDLP-Sinn Fein exchanges last week after receiving a report from Mr Hume, and is to assess the progress made at a cabinet meeting tomorrow.
But the discussions have been bitterly attacked by Unionist politicians in Northern Ireland.
In an Irish radio interview Sir Patrick continued to distance himself from the process, saying: 'I respect John Hume's record and think he is the best judge of whom he talks to.'
He said the only message the British government would be interested in from Sinn Fein or the IRA was that the violence was to end for good. He insisted that all- party, cross-border talks halted almost a year ago were not dead, and represented the best way forward.
Of Unionist warnings that the Hume-Adams meetings could block resumption of the broader talks process, Sir Patrick said: 'I do think that if the Hume-Adams talks are seen as an obstacle, then to that extent it would be better if they did not continue.'
An opinion poll in Dublin's Sunday Independent newspaper, by Irish Marketing Surveys, showed that 72 per cent of the electorate in the Irish Republic approved of the Hume-Adams talks.