The former Celtic and Aston Villa boss has been strongly linked with the vacant Republic of Ireland post and the FAI chief executive has singled the Derry man out for praise
O'Neill, 61, has emerged as the favourite to replace Giovanni Trapattoni as manager of the Boys in Green and recently said that he was "ready to go" when asked if he sought a return to management. Despite his refusal to reveal details, Delaney admitted that the Derry native was a man he "admire[d]."
"I have no problem saying that Martin O'Neill has been a terrific manager in his career, a terrific man and I admire him very, very much," he said. "But I wouldn't comment on Martin O'Neill or any other person as to whether they will be the next Ireland manager because that would be unfair.
"We are in a process. I would love today to be announcing whoever the new manager is if that were possible, but it's not.
"It will take a little bit of time given the fact the board of the FAI have yet to meet. We will look at the job description, who has applied and then the process as to how to appoint.
"I won't comment on any individual one, but what I will say about Martin O'Neill is that he is a terrific manager and has had a great career in football, both as a player and a manager."
In addition to Martin O'Neill, other candidates have been suggested, with former Valencia and Inter Milan boss Hector Cuper reportedly interested in the role.
Another potential candidate is Roy Keane, who is currently out of management following spells at Sunderland and Ipswich. The former Ireland international has been extremely vocal in his criticism of the FAI, and Delaney in particular, but the chief executive said that he would not let personal relationships get in the way of a managerial appointment.
"It's not a question of whether I could [work with Keane]," said Delaney. "Saipan is gone now and people have to forget about it. To be fair to him, he gets asked about it, which is why he comments. I will work with whoever is presented to us to make Irish football great.
"No personality issues that may have been there in the past should stop people working together for the sake of Irish football."
Delaney is currently with an FAI delegation in Croatia for a Uefa summit before returning to Ireland for an event in Galway on Thursday. It remains unclear when the board will formally meet to appoint a new manager.