Both clubs share the confidence that an agreement can be reached and a formal bid is expected from Chelsea in the near future.
Chelsea co-owner Todd Boehly, who bought the club earlier this summer as part of a consortium with Clearlake Capital, is involved in the negotiations and in contact with City to understand what fee they will charge Sterling.
The 27-year-old has been with the Etihad for the last 12 months of his current deal and is open to the prospect of a move to Chelsea, although he is currently weighing his options.
Manchester City will want to hold out for a substantial fee for Sterling after paying £ 45 million by agreeing to sell Gabriel Jesus to Arsenal, who also have one year to run on his contract.
Chelsea want to strengthen their forward line this summer and Sterling has emerged as a leading target for manager Thomas Tuchel.
The club have already agreed to loan out striker Romelu Lukaku, who is nearing a return to Inter Milan.