The Belgian led City to the Premier League title last season before leaving to take on a player-manager role with Anderlecht.
In his new book, 'Treble Triumph' Vincent Kompany: My Inside Story of Manchester City's Greatest Ever Season, which is being serialised in The Sun, the defender admitted his team-mates wanted him to stay put.
He said: "I had no idea if Pep (Guardiola) felt the same, or if he'd have been happy for me to carry on playing beyond that season.
"It was this ongoing fight to prove myself as being worthy of a place in the City team that led me to my conclusion — "I'm going to have to leave".
"The biggest compliment I've ever had was from David (Silva). He tried to convince me not to leave City.
"Sergio (Aguero) did the same. To have big players like that asking me to stay was absolutely the best thing."