The 29-year-old joined Manchester City last year and acquitted himself well in his first season at the Etihad, scoring 23 goals in 49 appearances following his move from Sevilla.
But Negredo, who is currently out injured, appears to have grown unsettled in England and is thought to be prepared to take a pay-cut to force through a loan move to Valencia.
If that happens, Sky Sports' Spanish football pundit Guillem Balague expects City to make a late Deadline Day swoop for Monaco’s Colombian striker Radamel Falcao.
Speaking ahead of Barcelona’s game at Villarreal, Balague told Sky Sports: “Negredo is negotiating with Valencia, with the possibility of going on loan and he is prepared to reduce his wages.
“And if that happens, Manchester City will then get Falcao.
“That’s the situation that is being negotiated at the moment. Everybody at the moment is still saying it is very unlikely, but Negredo is pushing to go Valencia.”
But a source at Manchester City has told Sky Sports News HQ they are not in negotiations with Falcao adding the former Atletico striker will not be going to City in this transfer window.
Keep up with all the latest transfer news and rumours on Deadline Day - coverage throughout the day on Sky Sports News HQ until the 11pm deadline with guests including Jamie Carragher, Jamie Redknapp, Rene Meulensteen, Christian Purslow, Guillem Balague and Niall Quinn.