The Blues are believed to be in talks with the Citizens over a deal worth around £45m for the 27-year-old, while the player is already understood to have agreed personal terms over a move to Stamford Bridge.
According to the Daily Mail, Chelsea are hopeful of finalising a deal for Ake, but Man City are delaying the defender's departure as they are looking to find a replacement first.
It is thought that RB Leipzig's Josko Gvardiol is one of Pep Guardiola's primary targets to replace Ake, but the report adds that a move for the Croatia international is unlikely as he is set to agree a new long-term contract with the German outfit.
City may now turn their attention to other targets and have been linked with the likes of Juventus' Matthijs de Ligt and Sevilla's Jules Kounde, who are also believed to be on Chelsea's radar.
While Ake's potential transfer is currently on hold, Thomas Tuchel's side are edging closer to signing Man City forward Raheem Sterling, as the Englishman is understood to have completed the first part of his medical on Sunday ahead of a proposed £50m switch to West London.