Alan Hutton has signed a new three-year deal with Aston Villa, completing an amazing U-turn by the club.
Rodwell's future at City has been the subject of constant speculation after failing to establish himself at the Etihad Stadium.
The 23-year-old has only started seven Premier League games for City since arriving from Everton in August 2012 and is thought to be keen on moving on this summer in a bid to get his career back on track.
Irvine knows Rodwell well having worked with the player during his time as assistant manager at Everton and he has described the midfielder as a "Rolls-Royce" of a player.
"I know Jack really well. He started training as a 16-year-old with the first team," Irvine told the Mirror.
"Jack is a very good player. He has had some injuries but he was a Rolls-Royce as a kid. Manchester City bought him for a huge amount of money so I can't imagine he is someone who will be available for a small fee."
The likes of Rodwell's former club Everton and Newcastle are also thought to be tracking the midfield dynamo this summer.
"Dynamo midfielder" ?? lol he was never that, remember he was always a defender and Moyes started playing him in mid to give him some spacial awareness. Don't want him back tbh- intermenan