Third-placed Lyon, formerly the great powerhouses of French football having won seven titles in a row between 2002 and 2008, lost 2-0 at mid-table Toulouse last weekend and had two players sent off.
The harrowing defeat left them seven points behind leaders Lille and six adrift of defending champions Marseille with five games remaining and speculation was rife this week that Puel, already unsure of his long-term future, could be axed.
"I never envisaged sacking him," Lyon president Jean-Michel Aulas told L'Equipe.
"There's no reason. We are third, five games from the end. People rang me Monday evening asking about this rumour, but it's absurd." Puel has previously said he may not remain beyond the end of the season and Aulas reiterated that the coach's future would be discussed only after the final game of the campaign.
Aulas was taken ill just after the Toulouse defeat but is now feeling fit and ready to try to inspire his troops to victory at home to Didier Deschamps' Marseille, who also dropped points last weekend.
"There are no excuses, we are all guilty and it's for this reason we are going to have a proud reaction against Marseille on Sunday," Aulas added.
Marseille were held 1-1 at home by struggling Auxerre on Sunday to hand Lille the initiative back in the title race but the lure of one of the biggest fixtures in the French calendar should be the perfect fillip for Deschamps' men.
Lille, meanwhile, hope their two rivals cancel each other out as they look to extend their advantage at third-bottom AS Nancy on Saturday.
The Mastiffs had suffered a wobble to let Marseille take over their long-time lead but last Saturday's 5-0 thumping of relegated Arles-Avignon powered them back to the top.
