The two North-Rhine Westphalian rivals meet for the 141st time on Saturday in one of the most eagerly-anticipated games on the Bundesliga calendar.
Schalke go into the game with a two-point advantage over the double winners, and Tonnies says two-time defending champions Dortmund are failing to live up to expectations because of Klopp's antics.
"They are under a lot of pressure," he said. "They have not been able to play with as much freedom recently because of this.
"Jurgen Klopp is an excellent coach and he has won the title twice in a row, but his permanent emotional body language is only increasing the weight of expectation.
"They are currently stumbling over these expectations and they are on thin ice in the battle for the title."
In fact, Tonnies believes Dortmund can already end all hopes they have of winning the title for a third straight season.
"Whoever thinks now that Bayern Munich will not win the league is detached from reality and is dreaming," he told Sport Bild magazine.
"That has got to be accepted."