The Blues identified the young English attacker as an ideal attacking addition this summer and are prepared to pay City for his services with the money recouped from the sale of Callum Hudson-Odoi used to finance the deal.
Chelsea have agreed to sell Hudson-Odoi to Nottingham Forest, and they will now focus on signing Palmer from City. The England under-21 starlet can play wide and centrally.
Mauricio Pochettino’s side reached an agreement after seeing their opening £35m approach rejected by City. Pep Guardiola’s side valued Palmer at £50m, but Chelsea hoped they would settle slightly lower. But according to Daily Mail, both sides reached a compromise for the 21-year-old of an initial £40m fee with a further £5m due in add-ons.
Palmer had already been the subject of summer interest from Premier League duo Brighton and West Ham.
City manager Pep Guardiola admitted earlier this month that Palmer, who has shown his qualities with goals in the Community Shield against Arsenal and Super Cup against Sevilla, could leave permanently this summer.
Guardiola said: “I don’t know [if he will stay]. I don’t think a loan is going to happen. He’s going to stay, or he’s going to be sold.”