Thomas Tuchel is keen to add more defenders to his squad and Chelsea have already wrapped up a €40 million (£33.8m) deal to sign Kalidou Koulibaly from Napoli.
Chelsea have also targeted Ake and have already held talks with City over a deal for the Netherlands international this summer.
But according to The Athletic, both City and Ake have come to a ‘mutual decision’ for him to remain with Pep Guardiola’s side.
The report claims that City were unwilling to sell Ake unless their valuation was met, while the 27-year-old is ‘pleased’ to be staying in Manchester.
Ake started just 10 games in the Premier League last season but is considered a valuable member of the squad due to his versatility.
Chelsea are now likely to focus on completing a deal with Paris Saint-Germain for Presnel Kimpembe.
It’s understood that PSG want a €50m (£42.3m) fee for Kimpembe.
Speaking during Chelsea’s pre-season training camp in Los Angeles this week, Tuchel made it clear that strengthening his defence is the main focus.
‘The priority right now is defence, it’s not a secret. From there we need to see what’s possible,’ Tuchel said.
‘We’re competing against the two top teams but Tottenham did a very active and aggressive and early transfer period, they have maybe the strongest squad they ever had with one of the best coaches in the world,
‘Man United are never shy of recruiting with a new coach and Arsenal had some big signings already so we need to keep the level up to be competitive.’
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