Crystal Palace have completed the signing of Lille left-back Pape Souare.
Football Association of Ireland chief executive John Delaney admits they could appoint another overseas manager to succeed Giovanni Trapattoni - but are in no rush to make a decision.
Trapattoni and the FAI parted company after five and a half years on Wednesday with qualification for next summer's World Cup finals in Brazil no longer a realistic possibility.
Delaney would ideally like to have a new man in place for next month's World Cup qualifiers, as the Republic start to rebuild with the target of Euro 2016 qualification in mind.
"This campaign was a disappointment. But we have a good set of young players coming through," Delaney told Sky Sports News.
"The overall context would be that Trapattoni was a success. There were two very good campaigns and one very disappointing one.
"In terms of the next manager, all we want is the best man. It doesn't matter if he's Irish, English, continental or whatever as long as we get the best man in to qualify for Euro 2016. That's what the Irish public want."
Several managers have already been linked to the newly vacant post, although Leeds boss Brian McDermott ruled himself out on Thursday, saying he is "100 per cent" committed to the Sky Bet Championship club.
However, Delaney refused to pinpoint who is his preferred candidate for the role, instead preferring to take some time to reflect.
He said: "There is plenty of speculation and there will be plenty of names, like Chris Hughton, Martin O'Neill, Mick McCarthy, Roy Keane and Brian McDermott.
"All those men will be mentioned. What we will do, the FA board will sit down over the next week or so, put together the type of job description that we want, the process and timing towards that.
"Ideally it would be nice to have a manager in place for the games in October but that's not a must because it's 12 months until we play our first European qualifiers in September. It's important that we get the right man in so we qualify for France 2016.
"It's best that we just reflect over the next four or five days. I'm going to ask my board members to go and speak to the grass roots. It's going to be a mix of everyone's views but in the next week the FAI board will decide the process of how we will go about the appointment.
"It's been a traumatic four or five days for Irish football and it's time to reflect now."
When asked if Keane, who was sent home from the McCarthy's 2002 World Cup squad following a bust-up with the then manager, would be in the frame for the role, Delaney said: "It would be an interesting appointment but it's probably inappropriate for me to comment on individuals because if I start talking about one being ruled in or ruled out that wouldn't be correct for me.
"We are going to get a new manager and that manager's objectives will be to get us to the European Championship in 2016.
"Football as we all know tends to surprise us but I wouldn't read anything in to someone being a favourite or not being a favourite."