Clermont chief Eric de Cromieres suggested on Tuesday the Top 14 season was over, after French President Emmanuel Macron extended the coronavirus lockdown until 11 May.
The league has been postponed since 13 March due to the Covid-19 outbreak with nine rounds of the regular season to play.
"Concretely, the championship is finished and we can't play again," the club's president told radio station France Bleu, after Macron also announced on Monday public gatherings would be banned until mid-July.
"It doesn't seem possible for me to train players in a contact situation, with scrums, with rucks by respecting the medical rules which have been put on us.
"For me it's not possible for players to train and be ready to play again in June," he added.
Club presidents are to meet on Wednesday when a return date for the campaign and moving the Top 14 final from 26 June to 18 July are on the agenda.
Laurent Marti of league leaders Bordeaux-Begles said he would like the campaign ended on the field.
"A majority of presidents want to end the season and have the play-offs and if possible find way that they won't be played behind closed doors," he told AFP on Tuesday.
"We might have to move the end of the Top 14 season back even more. July 18 remains an option. I don't yet know what will be discussed but we have to consider all options," he added.
Brive's Simon Gillham told newspaper Midi Olympique this week he was pulling out of the negotiations because of leaks to the media from previous video calls.
On Sunday, the director of French sport's financial watchdog (DNACG) Dominique Debreyer told the same paper nine sides could face serious issues ahead of next season.
The outfits will be unable to pay squad wages due to the lack of income caused by the pandemic according to Debreyer.
"We have to save French rugby. 80% of a club's expenditure is player salaries," Marti told AFP.
"Next year, we will obviously be faced with big financial problems. We can't ignore that, and everyone has to play the game, if not there's going to be some damage," he added.
France has registered nearly 15 000 deaths due to coronavirus with over 136 000 infected up to Monday.