The 23-year-old star was close to tears after captaining his side and scoring a goal in their win over Moreirense
Dias, 23, has been followed closely by City scouts for several seasons thanks to his exploits in the middle of defence at Benfica.
Dias, who represented Portugal at the 2018 World Cup, could command a transfer fee of up to €55 million (£50m/$64m), although City would also be keen to include Nicolas Otamendi as a makeweight in the deal in the hope of sealing a lower asking price.
While there has been no official confirmation over a deal being struck, Dias’ reaction on Saturday to questioning following his side’s Liga NOS clash hinted that his time at Estadio da Luz was coming to a close.
“I am very happy, obviously,” the Benfica captain, who appeared to be on the verge of tears during his brief interview, told BTV after netting in his side’s 2-0 win over Moreirense.
“This was a very important game for me, and to be able to crown it with a goal… it was a special moment.
“I think that everyone here will be able to guess why that is.
“It was without a doubt something special. The captain’s armband too was special.”
Benfica coach Jorge Jesus also recognised after the game that Dias would soon be leaving, telling reporters: “I am almost certain this was his last game. Sometimes in football everything can change at the last minute, but I don’t think this is the case.
“We are sad to see him go. He is a [Benfica academy] Seixal product, a captain, an international… But I am also to blame for him leaving.
“It is related to our Champions League elimination, there are things that have to be balanced and Ruben has a lot of market value.”
The defender has been with Benfica since the age of 11, joining from hometown boys’ club Estrela da Amadora in the suburbs of capital city Lisbon.
He has gone on to make more than 130 appearances at the club, forming a key part of the Benfica team that took the 2018-19 Primeira Liga title.
At international level the centre-back made his senior bow with Portugal in 2018 having represented the Selecao at every level from U-16 to 21, and currently boasts 19 caps as well as the 2019 UEFA Nations League crown.