With Martin O'Neill having departed the Ireland job "with a heavy heart" speculation is mounting on who will be his replacement.
Mick McCarthy and Stephen Kenny have already emerged as the favourites to take over the role.
It is understood the FAI would like someone in place for the Euro 2020 qualifying draw, which takes place on December 2.
Press Association Sport said it understands McCarthy is interested in the vacancy, returning to the job he held from 1996 to 2002.
Although, PA added he has recently rejected approaches from two English clubs.
McCarthy, however, responded enthusiastically two years ago when he was asked about a return to the team he took to the World Cup in 2002.
Liam Mackey of the Irish Examiner asked McCarthy if he would be interested and he said: "If there’s no manager in it and I’m out of work and someone asked me to do it, of course I’d do it."
He went on to add that if he did return, it wouldn't be because of felt he might have unfinished business with Ireland.
"Oh, I’ve got no unfinished business," he said. "I mean, to be unfinished I’d have to get to the quarter-finals or semi-finals of a World Cup to improve on what I did before, or get to European Championships because I didn’t qualify.
"That’s the only one regret I have, that we didn’t qualify when we were 1-0 up in Macedonia (in the 1999 game that ended with Ireland conceding an injury-time equaliser). No other regrets at all from my time in the job."