The duo were named after Bruno Genesio’s contract was not renewed last season.
Coach Sylvinho and sports director Juninho are under tremendous pressure after Olympique Lyonnais were beaten 1-0 by bitter rivals St Etienne, stretching the club's Ligue 1 winless streak to seven games.
The duo were named after Bruno Genesio's contract was not renewed last season, and the return of club darling Juninho, a fan favorite during his 2001-08 stay, had raised hopes that OL would challenge Paris St Germain.
After scoring nine goals and conceding none in two opening victories, Lyon looked like a decent challenger for the title, but things unraveled quickly.
Since then, they have picked up three points from seven matches and look a far cry from the aggressive team they had been under Genesio and his predecessors.
Lyon now lie 14th in the standings on nine points, 12 points from champions PSG.
Last week's 2-0 win at RB Leipzig in the Champions League bought the staff some time, but their loss in France's fiercest derby has put Sylvinho and Juninho back in the crossfire.
"We have rarely been in that situation. Juninho will have to think. We are not where we wanted to be, that's for sure," president Jean-Michel Aulas was quoted as saying by sports daily L'Equipe on Monday.
When asked if a change of coach was necessary, Aulas said Juninho would need to come up with a solution.
"You should ask Juni. He's shaken up because he had high hopes when he arrived. But we cannot do nothing," Aulas explained.
Lyon's derby defeat is particularly bitter as St Etienne are coached by Claude Puel, who was sacked by Aulas as OL coach in 2011 and was appointed by St Etienne two days before the game.
"The defeat hurt the fans. They must be like me, disappointed and distraught," said Aulas.