The Blues are currently third in the league table, one point behind City and three behind leaders United.
"It looks like that [it will be a three-horse race]," Cech told Chelsea's official website. 'We had a very good start.
"Manchester United started with a defeat but are now top and City had a very good victory because losing 1-0 you think Tottenham might get something out of the game but they managed to win and now have the advantage over us.
"It's early days and we still have to play them in two weeks, which will be a big game for both teams."
Chelsea finished sixth in the Premier League last season.