The Brazilian has emerged as top target for Pep Guardiola as he seeks reliability and stability in a key area of the field.
Claudio Bravo has flopped in the Premier League, while Joe Hart is expected to be offloaded once he returns from a loan spell at Torino.
Ederson could be the man to take the number one spot at the Etihad Stadium, with Goal revealing on Saturday that the 23-year-old is close to sealing a transfer worth upwards of £35 million .
“I still don't know but this was probably my last game for Benfica,” a man capped at U23 level by his country told RTP following a 2-1 victory over Vitoria on Sunday.
If he is to depart, then Ederson will leave Benfica as a double winner.
He helped them to league and cup glory in 2016-17, taking in 34 appearances across all competitions.
Benfica boss Rui Vitoria appears to think that an agreement will be reached, as he told reporters on the highly-rated keeper: "If Ederson leaves, he leaves with the gratitude of Benfica.
“He will always carry Benfica's name everywhere."
City have already announced a deal for Bernardo Silva and have a number of others in the pipeline.
Silva could be followed to the Etihad Stadium by former Monaco team-mate Benjamin Mendy, with Guardiola having positions to fill across his defensive line in the wake of several players being released.