Trapattoni, who the newspaper said was on a 1.8 million euro a year contract, had agreed to the cut after speaking with the Football Association of Ireland's (FAI) general secretary John Delaney.
"John spoke with me and said: 'The FAI has a problem, what do you think about agreeing to reduce your agreement because of this situation?'" the paper reported Trapattoni as saying.
"I said that we could discuss this and accept this... I think this is right."
No one from the FAI was available to comment.
Ireland recently agreed an 85 billion euro EU/IMF bailout, which will require unpopular tax hikes and spending cuts to pull the country out of a record-breaking recession.
The newspaper said pay cuts "in excess of five percent" would also apply to other members of the football management such as Marco Tardelli and Fausto Rossi, as well as Irish members Mick Martin and Don Givens.
Sports Minister Mary Hanafin welcomed Trapattoni's move.
"There are people in this country who are earning over half a million - 1.8 million euros in Giovanni Trapattoni's case - and there's absolutely no justification for those high levels at all," she was quoted as saying.
Trapattoni's current contract takes him to the end of the European Championships in 2012.
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