Sinclair impressed at Swansea City last year to earn a lucrative move to the Premier League champions, but Summerbee believes that Sinclair will need to prove himself to replace Adam Johnson, who has left to join Sunderland.
Summerbee told Manchester Evening News: "It's not the case that I think City have weakened, but he has to prove himself. He's come from a smaller club. It didn't happen for him at Chelsea, but he's proved himself away from there.
"I hope he brings the form he's shown already and do it at a bigger club, but Adam Johnson has proved himself for England and at crucial periods last season he was an important part of the squad.
"He set up goals, he scored goals. In my mind he's ahead of Sinclair. He's a better player, but I hope I'm proved wrong."
Sinclair could make his debut for Manchester City when they play Stoke City on September 15.