Mourinho subbed captain John Terry at half-time during the defeat at the Etihad and was accused of sending a message to owner Roman Abramovich over new signings.
Jose Mourinho is desperate for new signings at Chelsea
Express Sport understands the Toffees will reject that offer but could let the England international leave for a fee closer to £40m.
Mourinho is also keen on signing a striker and likes £21m-rated Lyon hitman Alexandre Lacazette and Atletico Madrid forward Antoine Griezmann.
Chelsea have finally completed a £21.7m deal for Augsburg left-back Baba Rahman, who replaces Filipe Luis at Stamford Bridge following his return to Atletico.
Rahman could make his debut against West Brom on Sunday (1.30pm), where Terry is also expected to feature.
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