Lyon president Jean-Michel Aulas said he will wait until the end of the season to decide the future of coach Bruno Genesio following Tuesday's 3-2 defeat at home to Rennes in the French Cup semi-finals.
Rennes twice led at the Groupama Stadium through goals from Mbaye Niang and Benjamin Andre, but Lyon hit back with a Bertrand Traore goal and Moussa Dembele penalty.
Algeria defender Ramy Bensebaini drilled home the winner for Rennes on 81 minutes to send his side through to the final and a possible showdown with holders Paris Saint-Germain.
Bensebaini's strike allowed Rennes to avenge Friday's 1-0 league defeat by Lyon and denied Genesio's side the chance to claim their first silverware since lifting the trophy in 2012.
"It was agreed that if we were in the final -- which is no longer the case -- and if we were in the top three, there would be a two-year extension," Aulas said afterwards.
"The deal that was reached with Bruno is that there will not be a contract renewal between now and the end of the season.
"It will stay like that. It's really sad not to be able to say that Bruno will extend his stay."
Lyon are third in Ligue 1 and trail Lille by four points in the race for the second automatic Champions League qualifying spot.
"I'm very disappointed we're not through to the final," said Genesio, who has been in charge at Lyon since December 2015.
"There are eight games left in the league and I'm going to do everything to lead the team into the Champions League.
"My personal situation is not the priority. We're not in control of our destiny because we're third. The goal is to be less than three points adrift of Lille when they come to play us (in early May)."
Rennes will face either four-time reigning champions PSG or Nantes, who meet in Paris on Wednesday, in the French Cup final at the Stade de France on April 27.
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