Ireland skipper Robbie Keane admitted on Monday that he would welcome the appointment of any member of that trio after urging the Football Association of Ireland to go for a man who would take a bold and fearless approach to the job.

Keane cited McCarthy as an example of a man who would bring just those qualities to the table, and Dunne agrees.

Asked if the current Ipswich boss was a realistic contender, the QPR defender said: “I think so, yes.

“He obviously said he might be interested, maybe, in it and having worked with him before, I really enjoyed it, so if he was the FAI’s choice, that would be great.

“I think we have got a good squad and it just needs putting into place, really, the team with a leader we can look to and hopefully someone who can guide us to more tournaments.”

The Republic completed their World Cup qualifying campaign on Tuesday night with a 3-1 Group C victory over Kazakhstan at the Aviva Stadium.

They did so with interim manager Noel King at the helm following the FAI’s decision to dispense with 74-year-old Giovanni Trapattoni’s services last month after back-to-back defeats by Sweden and Austria meant their hopes of making it to Brazil next summer were effectively over.

The mathematical doubt, as unlikely as it was, was finally removed by a 3-0 defeat in Germany on Friday, leaving only the issue of seeding for the Euro 2016 qualifying draw and pride at stake against the Kazakhs.

King left the Aviva Stadium expecting to return to his role as Under-21s manager as the focus shifted back to the search for Trapattoni’s replacement, which is being carried out by high performance director Ruud Dokter and former international Ray Houghton.

Keane, who set out the job description from the players’ point of view so eloquently earlier this week, is anticipating a reasonably quick resolution to the situation with two friendly games in the pipeline during next month’s international break.

The 33-year-old striker said: “Probably the friendly games, you would imagine they would probably have a new manager in by then because it wouldn’t make sense, really, to have two friendly games if you didn’t have a new manager in.

“We are what we are, we know who we have, so the new manager coming in, he needs to get his feet under the table and see what players are available to him and what players have to offer.

“It makes sense, probably, to have the manager before the two friendly games.”

Putting the new man in place in time for the November fixtures would give him time to assess what he has at his disposal and how he wants to play with the new qualifying campaign not due to get under way until September next year.

Dunne said: “There are a lot of things to be done over the next 11 months. I think the squad will probably be re-shaped and restructured and a new style of play, whatever the new manager wants.

“It gives us time to try to build and to make sure that come next September, we are ready to go.”

Keane, who won his 130th cap and collected his 61st senior goal – both are national records – against Kazakhstan, has already indicated he intends to play on in the quest for a trip to a second successive European Championship finals.

Dunne, who missed all of last season through injury, has no desire to hang up his boots just yet, but admits there will come a time when the decision may no longer be his to make.

Asked if he too would continue, he said: “I’d like to, yes.

“Obviously, I will get to an age where it’s not in my hands anymore. Whoever comes in might want a fresh start and new players, so I will just have to wait and see whether I am selected or not.

“But I don’t feel there’s any need for anyone to come out and make big statements that they are retiring or that they are this or that.

“I’m either picked or I’m not, it’s not really down to me.”