Rooney feels the former City captain could still have made a major contribution this season.
He said on Amazon Prime: "There's always a time when players leave the football club, and I think at this moment in time, with Man City going through this blip they are going through, and Kyle Walker being the captain of the club, and the importance of him over the last few years, I think, probably an agreement to say, 'Okay, let's wait till the summer. Help us out'. Maybe the league is too far out of their reach now, but they've still got the Champions League. Help us get through the season.
"I had it with Mourinho. When I wasn't playing with Jose Mourinho, and I had the same conversation in January, and he said to me, 'stay to the end of season, I need you to help us in the Europa League'.
"It was hard for me to take, but I respected him for that, and we shook hands, and then I left at the end of the season. So I think that would have been a more sensible move for Kyle."