The Argentine striker will leave City after a decade at the end of the season and there has been speculation about the likes of Borussia Dortmund’s Erling Haaland and Tottenham's Harry Kane taking over, though manager Pep Guardiola has insisted they have no cash to spend on a replacement.
Retired England striker, Crouch, has admitted he can't understand why City would want to get rid of Aguero just yet.
Responding to a Twitter user who sent in a question asking if Crouch can see Aguero playing for another team, he wrote in his Sportsmail column for the Daily Mail: "It would be odd, Paul. Very odd. But I have learned over the years to be surprised by nothing in football and if Aguero was to end up at Chelsea, for example, you would have to applaud them for doing the business.
"I'm surprised Manchester City are ready to let him go. Yes, they have been dominant this season and are going to win a lot of trophies without having used him but, as I see it, Aguero still has two more years in him at this level in which he will score 20-plus goals.
"I think he will go to a club abroad and the fact Barcelona and Paris Saint-Germain are being linked with him shows what quality he has got. If he went to Chelsea, it would be like when Frank Lampard went in the opposite direction and signed for City on a free.
"It never looked right seeing Frank in that kit and it was weird when he scored against Chelsea at the Etihad. I'd have the same feelings with Aguero.
"He is a Manchester City legend and nothing should happen for that to change."