Delaney will hold talks about potential targets in the next few days, but has not ruled out early favourite Martin O'Neill - or a return for Mick McCarthy.
"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.
"There is plenty of speculation and plenty of names like Chris Hughton, Martin O'Neill, Roy Keane and Mick McCarthy; all those names have been mentioned as have many, many others.
"We will sit down in the next couple of weeks and put together the type of job description we want, the type of process and the timings we will put towards that.
"Ideally we would like to have a manager in place for the games in October but that's not a must, because we have 12 months before we play our first qualifiers next for Euro 2016 and I think it's important we get the right man in so we have the best chance to qualify for France in 2016.
"The players will have their views and the public will have different opinions too. It is going to be a mix of everybody's views. My board members will speak to the grassroots too.
"But ultimately the FAI board will decide in the next week or so how we go about making the selection. Last time Ray Houghton, Don Howe and Don Givens helped us make the decision. We may use a similar process this time, we may not.
"It's something that is very open and now is time for a short period of reflection about the job description, the process and the timing."
O'Neill is the current bookmakers favourite for the job but Delaney would not be drawn on his, or any other candidates', chances.
He said: "Roy Keane would be an interesting appointment but it would be inappropriate for me to start talking about individuals because as soon as I start talking about one then he will be ruled in or out. That wouldn't be correct of me.
"Mick McCarthy managed us before he was our second most successful international manager and Giovanni Trapattoni would be our third. Jack Charlton was our first. Mick is a good man and has done well both at international level and at club level.
"This morning, my phone was ringing and names were being put into the hat and that is the way the process works. We must be as confidential as we can. If you remember last time, Trapatonni came out of nowhere and there were six or seven different favourites through the whole process."