Cech, now a football adviser with the Blues, was asked by the club's website about his toughest opponent.
He replied: "Wayne Rooney.
"Every time we played against United I had to make sure I was aware every time he had the ball, because he was very unpredictable and very clever.
"He is a guy who can chase, who can fight, who can run, who is clever with his shot. He could score from the halfway line, he could try and chip you if you were too high. That was a challenge I enjoyed."
Rooney is now player-coach with Derby County.
Cech believes the Premier League has been the best competition in the world for over ten years.
He added: "The league has got more competitive.
"When I came in 2004, probably the top 12 teams were very strong, with strong squads, and then it would really depend on the years for the other eight teams. For them it was harder to bring in international players.
"It started changing around 2007, 2008 when the Premier League's dominance started. You would suddenly see international players coming to every team, even promoted teams. The league became a big attraction. Teams started getting stronger and stronger, and the competition became harder and harder every year. That has continued to this day. It's what makes the Premier League the best."