Dias will become the most expensive player in City's history - eclipsing the £62.8m paid to Atletico Madrid for Rodri a year ago - with Nicolas Otamendi joining Benfica for £13.7m as part of the deal.
The 23-year-old Portugal international has passed a medical but the transfer will only go through once Otamendi has been given the all-clear by his new club.
City's 5-2 capitulation at home to Leicester on Sunday underlined the need to strengthen at the back despite spending £40m on Nathan Ake from Bournemouth.
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