The report says that Newcastle boss Sir Bobby Robson tabled a bid of £3.5m.
Robson said: "The possible purchase of Rooney will not stop us bringing in a centre-half.
"We're aware of what we've lost and we're fully aware we need a replacement and we're working on that - but you will appreciate it's not easy.
"We're looking for a genuine quality player, someone who can play in the Premiership and who doesn't have to be long-term.
The proof will be tonight if Davenport does not play in City's Football League Cup tie against Torquay United at Highfield Road and therefore is not cup-tied. However,it is believed that the popular central defender may hold out until January so that he will got most of the transfer himself.