The midfielder is widely expected to leave St James' Park before the new season begins after Sam Allardyce admitted he was suffering personal problems.
West Ham were the first club to register an interest but Dyer is thought to favour a move to Spurs, with Martin Jol tipped to launch a bid next week.
Sven-Goran Eriksson has also been strongly linked with the 28-year-old, who he knows well from his time in charge of England, but the City boss is not in the running, according to BBC Sport.
Dyer was left out of the Magpies squad for Thursday night's friendly with Celtic as Allardyce was "protecting the club's asset".
Allardyce insists no bid has yet been lodged, but the former Ipswich star will be allowed to leave for around £5million.