The outspoken former Oasis musician has called for the former Manchester United captain to prove that he "can do it better than anyone else" after his criticism of the team
Ireland crashed out at the group stage after failing to take a single point from their three matches, leaving Keane annoyed at the low standards demanded by the country.
Speaking in Croke Park ahead of his performance in support of the Red Hot Chili Peppers in Dublin, Gallagher revealed that he thought the former Sunderland and Ipswich manager should take the national team job.
"Roy [Keane] is pure comedy," he told the Irish Independent. "He should take over the Ireland job if he thinks he can do it better than anyone else."
He added: "I've never met him but he probably hates me like everybody else."
The musician is widely known to be a Manchester City fan, but expressed his admiration for Manchester United legend Keane as a player.
"He is easily one of the top five players that the Premier League has ever had," said Gallagher.
"I thought he was a great player for United. If only England had Roy Keane now, they would win games.
"He was the one player who could take a game by the scruff of the neck and bully his teammates from three goals down to win. He was immense."
Despite being born and raised in England, Noel Gallagher had a strong Irish upbringing and was an accomplished GAA footballer in his youth, even making an appearance at Croke Park in 1983 for Manchester club Oisin's in a game against Kilmacud Crokes.
Recalling the occasion, Gallagher said of Croke Park: "It's all done up now. I'm not sure there was even seats. I scored a point but I can't remember at which end."