Ex-Sunderland boss O'Neill is being widely tipped to replace the 74-year-old Italian, who left the role by mutual consent on Wednesday after consecutive defeats to Sweden and Austria left Ireland facing a tough task to reach the 2014 FIFA World Cup.
A Northern Ireland international in his playing days, O'Neill led Celtic to three Scottish titles, as well as three Scottish Cups, also securing two English League Cup wins with Leicester City.
He departed the Stadium of Light in March after an eight-game winless run that left the Wearside club facing a relegation dogfight - which they narrowly escaped under new boss Paolo Di Canio.
O'Neill has insisted that he is yet to be contacted by the Football Association of Ireland (FAI) about the role, but Ipswich Town boss McCarthy, who was in charge of Ireland from 1996 to 2002 and had been linked with a return, believes the former winger is a certainty.
"Martin has the job as far as I am aware. Absolutely nailed on, a shoo-in for it," McCarthy said.
"He is out of work and he is a good manager. So it is my understanding he has the job - so good luck to him."
McCarthy reacted indignantly when quizzed on his own links to the role, admitting that it was no shock to see his name among those being touted.
He said: "I am not surprised because I did a good job last time."
