The new Baggies boss said that he knows the player well from his stint as assistant manager at Everton, and was quick to lavish praise on him.
"I know Jack really well. He started training as a 16-year-old with the first team," The Mirror quotes him as saying.
"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."
Rodwell, who has only started seven games for City, has also been linked with Newcastle United and former club Everton.