Ireland are in the process of searching for a successor to Italian Giovanni Trapattoni, who departed the role by mutual consent in September after a 1-0 qualifying defeat to Austria all but ended their hopes of reaching the FIFA World Cup.
McCarthy is rumoured to be one of the candidates being considered, a move that would see him return to a position he held between 1996 and 2002.
And LA Galaxy striker Keane - who is his country's record scorer with 60 goals in 129 caps - would support the appointment, while also endorsing fellow hopefuls Martin O'Neill and Roy Keane.
"Why not with Mick, it (returning) happens a lot," said Keane. "Holland have done that a few times. Mick is a great guy, a fantastic guy.
"But if it was Mick, Martin O'Neill or Roy Keane, I don't think you can go wrong.
"As long as it's the right man it doesn't matter, but at this stage I think everybody would like an Irish manager.
"The names who have been mentioned, if any of them took over I think everybody would be happy.
"We need someone who is an honest manager, who doesn't mess around, someone who understands how important it is to be involved at international level, someone who is proud of what we are trying to achieve in Ireland. Someone who is honest."
Ireland sit in fourth position in Group C of the European World Cup qualifying section, and complete their campaign when they entertain Kazakhstan on Tuesday.
