Dunne, 28, is expected to leave City this summer and has been linked with Newcastle and Tottenham among others, but Redknapp is hoping the prospect of European football will tempt him to Fratton Park.
When asked if he is interested in Dunne, Redknapp told BBC Radio Five Live: "Very much, I like Richard Dunne. I think he´s a top player but I think there´s a couple of clubs in for him at the moment, but I think we´ve got as good a chance as anyone now."
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