Cash strapped Valencia are looking for as much money as they can get for the player and they are holding out for £30m but City, despite being the richest club on the planet, are reluctant to go to that price.
Cook is thought to have had a meeting with Valencia president Manuel Llorente as he tries to get £5m knocked off the asking price and there is also talk of using Paraguayan striker Roque Santa Cruz as part of the deal.
As City try and broker an agreement Chelsea sit quietly in the shadows waiting to pounce if the move collapses.
A goal apiece from James Tomkins and Luka Milivojevic handed Crystal Palace a crucial 2-0 win over Huddersfield at the John Smith's Stadium on Saturday evening.
Manchester United bounced back from their Champions League exit as they beat Brighton 2-0 at Old Trafford on Saturday night to reach the FA Cup semi-finals.
Tottenham reached the FA Cup semi-finals after they cruised to a 3-0 victory over Swansea in their quarter-final clash at the Liberty Stadium on Saturday.
Premier League basement club West Brom squandered the lead as they suffered a 2-1 defeat to Bournemouth at the Vitality Stadium on Saturday.