McCarthy and Keane fell out spectacularly at the 2002 World Cup when Keane left the Ireland camp before the team's first game.
Now the former Sunderland boss is reportedly just behind Keane in the reckoning to take over at the City Ground.
Keane is reportedly the first-choice of chairman Nigel Doughty, with England number two Tord Grip, former Forest boss Dave Bassett and current Oldham boss Ronnie Moore also in the frame.
The reports from Scotland do not tally with those from the Nottingham Evening Post earlier in the week which suggested that the Reds were after a younger manager with some experience for the post, with candidates such as Nigel Clough and Colin Calderwood in the frame.