Delaney said that the only factor that they are taking into account is the calibre of the candidate and whether he is from Ireland, England or elsewhere in Europe is not important.
"In terms of the next man all we want is the best manager," Delaney told Sky Sports News. "It does not matter whether he is Irish, English, continental or whatever.
"We want the best man in to get the best out of our players and get the team to the Euros in 2016. That's what the Irish public want, that's what the Irish soccer supporters want, that's what the Irish association wants."
Trapattoni left his post as Ireland manager on Wednesday night.