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The president of the club's board, Jean-Michel Aulas, acknowledged that the head coach Claude Puel cannot be calm about his future.
The multiple French champions currently occupy only 17th place in the national championship.
"For a strategist who fails to achieve results in Lyon, there is a threat," Aulas stated. "Five points in six games is not a good enough result, but let's not forget that we won our first Champions League match against Schalke in Gelsenkirchen."
"We will evaluate everything on November 23 - by then we will have played 10 matches in the French championship and three in the Champions League. If the results are not good, we will have to make changes."