The offer for Mangala, who is up for sale at the Etihad, is believed to be worth £18m with £5m in add-ons.
Palace’s deal for the 26-year-old indicates that they are ready to withdraw their interest in Liverpool’s Mamadou Sakho.
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Sakho spent the second half of last season on loan at Selhurst Park and became a fan favourite, making several impressive performances for Sam Allardyce’s side as they avoided relegation.
Liverpool's discussions with Palace on Tuesday made it clear that Palace must include more achievable add-ons, and the Reds want a deal that reaches £30m.
While the south Londoners would prefer to sign Sakho, a deal for Mangala would allow them to still fill some other positions of need - including a new goalkeeper and a back-up striker.
Mangala’s departure would allow City to finalise a move for West Bromwich Albion defender Jonny Evans.
Mangala cost City £41.4m from Porto in August 2014 but struggled to adapt to English football and spent last term on a season-long loan at Valencia.
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