The bank says it will not attend hearings of the inquiry because it does not answer to national parliaments.
Mr Draghi met with Enda Kenny at a summit in Brussels last night.
And the Taoiseach says the Christmas break for the inquiry gives Mr Draghi plenty of time to change his mind,
“I've asked him that he would consider how best the European Central Ban might be able to assist and contribute to the banking inquiry” he said.
“Obviously the programme of hearings has been set out by the committee and the chairman, and they will adhere to that”.
“There will be plenty of opportunity for Mr Draghi to give consideration as to how the ECB might be able to contribute” he added.