Martin O’Neill is the odds on favourite with the bookies betting in UK to replace the Italian who resigned yesterday after a 1-0 defeat in Austria ended any hopes of reaching the World Cup play-offs.
Kenny Dalglish and Liam Brady are rated at 40/1 but are joined at that price by Graeme Souness suggesting that their chances are slim.
Mick McCarthy, who managed Ireland at the 2002 World Cup, is second favourite to O’Neill at 15/2 with his former captain, Roy Keane, priced at 18/1.
Trapattoni took over from Steve Staunton in 2008 with the highlight of his reign taking Ireland to the 2012 European Championships in Poland.
Announcing his resignation the Italian said: “I want to thank everyone in Ireland who has given us their support during our time here, which has always meant a lot to us.
“We leave this country with emotion because we understand the Irish supporters who have a well-deserved international reputation and they have our utmost respect.”
Trapattoni’s salary was partly paid for by Celtic shareholder Denis O’Brien which has helped fuel speculation that O’Neill could be the next Irish manager.
O’Neill has managed Aston Villa and Sunderland since leaving Celtic but has been out of management since losing his job at The Stadium of Light in April.
In 2006 he was strongly linked with the England manager’s job but lost out to Steve McClaren.
Although he has been critical of international football in the past the chance to manage Ireland would have a lot of appeal for O’Neill as he sees younger men getting the top jobs in club management.