The Citizens were believed to be in pole position to acquire the Portugal international when it became clear that he would be leaving Juventus before the deadline.
However, Manchester United ultimately landed the 36-year-old, who has scored three times in his first two appearances since returning to the 20-time English champions.
"I think there was a good, considerable chance. I think his agent was here at the club renewing the contracts of Ederson, Ruben Dias, seeing the situation of Bernardo Silva, Joao Cancelo," Fernandinho told ESPN.
"Obviously, if you're there at the table, you can talk about everything and every possible player. I think that a lot of expectations were also raised with the possibility of him coming here.
"No doubt this ends up affecting not only the fans, but also the people inside the club. But in the end, things didn't work out, he didn't close the deal, and ended up going to the red side of town. Life goes on."
Man City opened their 2021-22 Champions League group-stage campaign with a 6-3 win over RB Leipzig on Wednesday night. body check tags ::