There was no immediate confirmation from City, who finished third in the Premier League this season under Spanish manager Pep Guardiola.
The fee would be close to the world record for a goalkeeper, with Juventus paying a reported 40.2 million euros when they signed Gianluigi Buffon from Serie A rivals Parma in 2001.
Benfica said also that half of the fee would be paid to unidentified 'third parties', an element that could slow completion of a deal.
Third party ownership, where part of a player's economic rights are owned by private investors, is not allowed under Premier League rules and that will need to be resolved before the player can be registered.
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City failed to win any silverware this season, the first time Guardiola has experienced such a drought in his managerial career, and are set to spend heavily over the summer to remodel their squad.
They have already paid Monaco a reported 43 million pounds for Portuguese midfielder Bernardo Silva.
Goalkeepers have been a particular headache for the Abu Dhabi-owned club, with England's Joe Hart sent out on loan to Torino at the start of the season and Chilean Claudio Bravo failing to convince in the role after being signed from Barcelona.
Willy Caballero, who replaced Bravo towards the end of the season, was one of four players released last Friday.
Media reports said Sao Paulo-born Ederson, who moved to Portugal as a 16-year-old and was at Rio Ave before returning to Benfica in 2015, had visited Manchester earlier in the week for a medical.
The summer transfer window opens officially in July.
(Reporting by Alan Baldwin in London; Editing by John O'Brien and Pritha Sarkar)
