French international Coupet was looking for a new improved contract at Stade Gerland, but, after consulting with his board, chairman Jean-Michel Aulas has confirmed that a new deal would not be forthcoming.
"He met with us the day we won the title," revealed Aulas. "The talks were really frank and he asked me if we were going to increase his wages and prolong his stay.
"After asking the opinion of the board of directors, I told him 'no' and I regret this statement.
"If he finds a new club, we will let him leave. There are serious talks in France and abroad, and his agent Pape Diouf should have plenty of propositions."
Sources in France are now suggesting that Arsenal will be able to use Coupet's situation to help find their new goalkeeper, although it is not the Lyon man being linked.
The man said to be again at the head of Arsene Wenger's wanted list is Monaco's Flavio Roma.
Monaco have just agreed a deal to sell Shabani Nonda to Lyon, but they are still looking to raise cash as they aim to preserve their league top-flight status.
The Principality club aim to prove to the French authorities on Wednesday that they are financially stable and avoid demotion to the Second Division.
Monaco already have a loan in place to cover their debts, but the sale of Nonda and possibly Roma would only help their cause.
Coupet is actually being linked with Monaco as replacement for Roma, with reports suggesting that Arsenal have already lodged a bid for the Stade Louis II shot-stopper.
It now remains to be seen whether The Gunners' interest is as concrete as French sources are suggesting.
Lyon are also gearing themselves for a number of departures and Aulas confirmed that both Marc-Vivien Foe and Florent Laville will be leaving.
Both enjoyed loan spells in England last season, Foe with Manchester City and Laville with Bolton, and the pair are widely expected to return to The Premiership this summer.
"Marc-Vivien Foe and Florent Laville will leave," he said.
"Edmilson could also leave, but we don't have any interesting propositions for him.
"Jeremie Brechet has also asked for a meeting about his future."
One player unlikely to leave is striker Sidney Govou.
"He told us what he had to tell us, it was very clear," Aulas continued.
"I am very happy with the player and he also wants to stay.
"I prefer a boy who wants to continue at Lyon because it is a great club."
