The official announcement is to be made at the Aviva Stadium at 15:00 GMT.
A bookmaker has McCarthy at odds of 1-12 to return to the job while RTE have reported that he is to sign a two-year contract.
The 59-year-old would succeed Martin O'Neill who left the role on Wednesday, along with his assistant Roy Keane.
The other main contender for the role had been thought to be Stephen Kenny, manager of Irish club Dundalk
The FAI wanted to make a swift appointment, with the draw for the Euro 2020 finals taking place in Dublin on 2 December.
Qualifying group fixtures start in March 2019, with Dublin one of the 12 cities due to host Championship matches the following year.
McCarthy, who stood down as boss of Ipswich Town in April, led the Republic to the last 16 of the 2002 World Cup.
He famously had a pre-tournament row with Roy Keane at a training camp in Saipan which resulted in the Irish skipper leaving the squad.
McCarthy quit later that year after the Republic made a poor start to the qualifying campaign for Euro 2004.
Since then he has been in charge of Sunderland, Wolverhampton Wanderers and Ipswich.
McCarthy's first spell as Ireland boss began in 1996 when he took over from Jack Charlton.
He is expected to have his long time assistant Terry Connor on his team, with a possible role for the Republic's all-time leading goal scorer Robbie Keane.