Irvine was appointed as Pepe Mel's successor at The Hawthorns last week and has since discussed plans to strengthen his squad in terms of quality and depth.
Having previously confirmed an interest in Rodwell's departing City team-mate Joleon Lescott, Irvine has hinted he may also be interested in signing the 23-year-old midfielder.
The pair worked together at Everton, where Irvine was assistant to David Moyes, and the West Brom boss made no secret of his admiration for Rodwell's quality.
"I know Jack really well. He started training as a 16-year-old with the first team," Irvine told The Daily 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."
Irvine has also declared his desire not to sell players before he has had a chance to assess his squad in pre-season.
Midfielder George Thorne has been linked with joining Championship side Derby County permanently, after spending the latter half of last season on loan at the iPro Stadium.
However, technical director Terry Burton told The Birmingham Mail: "He's Albion's player, he's under contract, we think he's a good player and we want the opportunity to see if we can give him first-team football.
"But that's up to George to show he's the best man for the role."
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