Mick McCarthy is known to be keen on returning to the Republic of Ireland manager’s job after Martin O’Neill left the role together with his assistants, including Roy Keane.

McCarthy, who played 57 times for the Republic and filled the position as manager with distinction for more than six years until his dismissal in 2002, is available after stepping down at Ipswich in April. Also out of work and said to be a candidate is Sam Allardyce, who began his managerial career in Ireland with Limerick and had one match in charge of England.

The Football Association of Ireland is understood to be keen on appointing a replacement before the Euro 2020 qualifying draw in Dublin on 2 December. Stephen Kenny, celebrated for the attractive style he has cultivated at the League of Ireland champions Dundalk, would be a popular and bold option. With the FAI loth to miss out on a tournament it is to help co-host, a manager with experience of international football would be a safer choice.

The departures of O’Neill and Keane followed talks on Tuesday between the pair and the FAI’s chief executive, John Delaney, who had awarded them contract extensions in January in recognition of the positive results achieved in their first four years.

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Results and performances have deteriorated since and Delaney, confronted with dwindling attendances, rising criticism and the prospect of missing out on Euro 2020, let O’Neill and Keane know he thought it was time to end their reign. Séamus McDonagh, the goalkeeping coach, and Steve Guppy, an assistant coach, have also gone.

“It is with a heavy heart that I leave this role,” O’Neill said. “It was one of my lifetime ambitions to take charge of the Irish senior squad and I would like to thank the FAI board for giving me that opportunity.” The 66-year-old added that he was “looking forward to my next adventure in football”.

Ireland have won only one of their past 11 matches and had been relegated from their Nations League group before Monday’s 0-0 draw in Denmark. O’Neill had tried to revamp his squad over the past year, giving debuts to a dozen players, and he said after the Denmark match that he remained enthusiastic about his role and confident of reaching Euro 2020, for which Ireland is one of 12 host nations.

Last month O’Neill went so far as to say he was certain he could lead Ireland into those finals, declaring: “We’ll go through. Simple as that. Because I’m good.” The FAI, however, will now entrust that task to someone else.

Ireland’s miserable performance over the past 12 months amounted to a sorry end to a tenure that previously delivered early success. O’Neill and Keane’s first campaign culminated in qualification for Euro 2016, where Ireland reached the knockout stage for the first time. They came within a play-off of reaching the 2018 World Cup after finishing second in a qualifying group for which they had started as No 4 seed. The heavy defeat in Dublin – 5-1 by Denmark – in the second leg of that play-off triggered a downward spiral that O’Neill and Keane were unable to stop. Criticism of a blustery style of play grew deeper.

Delaney said: “I would like to thank Martin, Roy, and the management team for the impact that they had with the Ireland team. There have been many highlights during Martin’s reign – none more so than Euro 2016 in France, which will live long in the memory of all Irish supporters. Martin did a great job guiding the team out of a difficult qualifying group – where we beat world champions Germany along the way – to reach Euro 2016 and advance to the last 16 following a historic victory over Italy in Lille.”