The former Germany boss feels that the Bundesliga champions could spring a surprise, while he also sees City as outsiders to go all the way in this season's competitionBorussia Dortmund and Manchester City have what it takes to cause an upset in the Champions League and win the competition.
Dortmund and City both stumbled at the first hurdle last term as they failed to advance beyond the group stages, but Klinsmann is confident they can do better this season.
"English champions Manchester City or Bundesliga champions Borussia Dortmund are teams to be reckoned with. They could cause a surprise and win the Champions League," Klinsmann stated to Spox.
"For example, I believe that Manchester City are a better team than Chelsea.
"As for Dortmund, they have to realise that the Champions League is something completely different than the Bundesliga.
"There are only six group games. It is going to be different when you're chasing right from the start. But Dortmund are in such a spectacular and even group that anything can happen.
"The most important thing in the Champions League is that you hit top form at the right moment. It's impossible for any team to be on top of their game the entire season. They key is to make sure your lesser performances do not occur when there are important Champions League encounters."
Borussia Dortmund kick off their Champions League campaign against Ajax on Tuesday, while Manchester City take on Real Madrid.