City are confident they will conclude negotiations for Ederson shortly after Benfica's Taca de Portugal final against Vitoria Guimaraes on Sunday.
And it has also emerged on Saturday afternoon that City agreed personal terms with Mendy during last week, despite rival interest from Manchester United.
It is also believed a move for Tottenham's Kyle Walker is close to completion.
City confirmed the signing of Bernardo Silva from Monaco on Friday and Goal has learned the club have prepared staff for another official announcement on Monday.
Whether the eventual fee surpasses the world record or not, City believe they are buying a goalkeeper who has the potential to be one of the very best in the world and, crucially, one who fits into Pep Guardiola's plans.
Benfica only own 50 per cent of the keeper's rights and are therefore holding out for as large a transfer fee as possible, as they will have to split half of the total between Rio Ave, the Brazilian's former club, and football agency Gestifute.
Mendy could cost City around £39m, with the Blues keen to finalise a deal as soon as possible having identified the 22-year-old as a priority target some time ago.
As with Bernardo Silva, who signed for £43m on Friday, the Blues have been working on deals for Ederson, Mendy and Walker in recent months and are now close to making official announcements long before the transfer window officially opens in July.
Ederson could arrive in Manchester at the start of next week following Sunday's cup final with Benfica. Jorge Mendes, who has been at City's training ground to facilitate Silva's move, is also the Brazilian's agent and owner of Gestifutre, and will help resolve any lingering third-party issues.
Given Ederson's rights are owned by a former club and Mendes' own company, City believe they will be able to find a swift resolution.
Although any transfer fee above £33m would represent a world record fee for a goalkeeper in pound sterling, Juventus actually bought Buffon for €55m, which is around €15m more in euros than Benfica could receive for Ederson.
Whatever the current conversion rates or potential records, City are ready to pay big money for their top targets this summer as they realise the best players on the market will be coveted by the biggest and richest clubs around Europe.
Guardiola has bemoaned the current state of the transfer market, highlighting the £38m Real Madrid paid for 16-year-old Brazilian Vinicius Junior, and City do not want to be drawn into lengthy negotiatons.
That is why they moved quickly to tie up a deal for Silva, and club insiders believe the £43m they paid to Monaco will be recognised as a bargain by the end of the summer.
They are of the same opinion regarding Ederson, Mendy and Walker, and are hopeful of finalising all three deals in the near future.
Additional reporting by Julien Quelen.