Nabil Fekir will be offered a new contract if he rejects interest from Liverpool to stay at Lyon.
Lyon broke off talks with Liverpool earlier this month as Fekir, whose contract with the seven-time French champions runs to 2020, prepared to head to Russia as part of France's World Cup squad.
The 24-year-old's agent said last week the deal could still be on, but Lyon president Jean-Michel Aulas is ready to push the boat out to keep his club captain.
"I had an exchange with him the day after the night when we decided to stop talks with Liverpool. He was very calm. I immediately told him that if he wanted to stay, we could extend his contract," Aulas told Le Parisien.
"I had said before that we don't need to sell. We have the means to keep Fekir. The current tendency is that we don't let anyone go so that we have a better team and we strengthen it as planned.
"There will be no arrivals before July 1. There will be departures, which will be added to the accounts which are very good, even without a star leaving. We have a very strong financial structure. If Nabil left, it would be the jackpot."
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