The deal for Dias, 23, will be worth between €60m and €65m and he will sign a long-term contract.
32-year-old Otamendi, who has been linked with Benfica’s rivals and his former club Porto, will move in the opposite direction.
City’s interest in Dias is nothing new and they had a €100m deal in place before the Coronavirus pandemic.
Dias has been a key figure in the heart of Benfica’s defence for the past three seasons and should this move be confirmed, will link up with compatriots Bernardo Silva and Joao Cancelo.
Despite his youth, Dias has already amassed 136 first-team appearances for Benfica, and 19 for Portugal.
Dias is regarded as one of the best young centre-backs in Europe and has been tracked by several major clubs.
City have been in search of a second central defensive recruit after signing Nathan Ake earlier in the summer.
City’s top target was Kalidou Koulibaly, but Napoli’s demands have cooled that track.