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.
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."
He said: "I am not surprised because I did a good job last time."
