The proposed fee is in the region of £45m, which would be a world record for a 'keeper.
Ederson soon deleted the Instagram Story post, as we await confirmation of the transfer from City.
It means City will go into the new season with some uncertainty over a position that is crucial, particularly after a year in which an inability to keep clean sheets proved so expensive to Guardiola's side.
Coach Rui Vitoria is expecting Ederson to leave the club, telling reporters: "If Ederson leaves, he leaves with the gratitude of Benfica".
The goalkeeper was called up by Brazil in March but has yet to be capped.
The Sao Paulo-native later moved up the ladder to top flight Rio Ave and ultimately re-signed for Benfica for a fee of just €500,000 in the summer of 2015. He was initially behind his fellow countryman Julio Cesar in the pecking order. He kept a clean sheet as Benfica claimed a vital 1-0 win.
Pep Guardiola is getting his business done early, having confirmed the signing of midfielder Bernardo Silva before the weekend, and he's about to make his second acquisition of the summer. Hart was sent on loan to Italian club Torino.
FA and Premier League bosses are scrutinising the paperwork before permission can be granted for the deal to be ratified. He has made some high profile mistakes and received criticism from pundits and supporters.
By then he'd lost his place in the Premier League to Caballero. Ederson has proven himself to be a capable goalkeeper.
How good has Ederson been this season?