Dias, 23, came through Benfica's academy and has been a regular in the club's senior side since the 2017-2018 campaign.
In that time he has reportedly been tracked by many of Europe's biggest clubs, including Manchester United, but it appears his next move will see him wear sky blue instead of red.
City is said to have offered €55 million ($89.1 million) and Nicolas Otamendi to Benfica for the highly-rated Dias, who is also a regular at international level with Portugal.
Dias scored the opening goal in Sunday's (AEST) victory and also wore the captain's armband, while he was shown sharing emotional embraces with Benfica icon Rui Costa and other members of the club's hierarchy at full-time.
Jesus then effectively confirmed Dias's exit when he spoke after the game.
"I would like to be absolutely sure, but it was almost certainly the last game he played," Jesus said.
"In football you never know, sometimes everything changes in the last second, but I think that will not happen. He is a player we are sorry to see leave. He's a great player.
"But I also have some fault for the departure, this has to do with the elimination from the Champions League [qualifiers] and there are things that have to be balanced.
"He is the only player who has a high market value. He is already a good player and will be a beautiful player."
Jesus also briefly discussed the chance of Otamandi joining from City, suggesting it will not be a swift adaptation period for the former Porto man.
"Of course, Ruben has had seven weeks with me. It was not easy at first for all of them to adapt to my idea of the game," he said.
"And when he [Otamendi] arrives, he will realise that my ideas are different from those of Manchester City. This is if the Manchester City player comes.
"There is also talk of Ruben Semedo. It will be weeks of adaptation."
A visibly emotional Dias savoured his moment with Costa and was thrilled to seemingly close the Benfica chapter of career in such a manner.
"It was a special moment [with Costa] and I think everyone already knows why," he said. "Obviously, people leave their mark on you, and the club also. Without a doubt, it was very special for me.
"I am very happy. It was very important to consecrate this game with a goal, it was very special for me."