Jean-Michel Aulas has admitted that Lyon were interested in signing Jose Antonio Reyes and Arjen Robben over the summer.
Reyes secured a move from Arsenal to Atletico Madrid during the transfer window, while Robben joined Real Madrid from Chelsea.
Aulas admits Robben was far too expensive in the end, but he had been hopeful on Reyes.
"We were looking for a left-sided player, but Robben didn't want to leave when we contacted Chelsea," Aulas told France Football.
"Anyway, could I have invested 35 or 37million euros on a boy like Robben, having (Hatem) Ben Arfa in our squad? No.
"We asked information about Reyes. But when we called Arsene Wenger he told us he already had a draft agreement signed with Atletico Madrid.
"From the start Arsene told us there was no chance."
Another transfer target for Lyon over the summer was Roma's Alessandro Mancini, and Aulas is optimistic of resurrecting a deal for the Brazilian in January.
"I went to Roma, I met him and let's say he and his agent agreed to join us," he explained.
"Mancini really wanted to come at Lyon, but Roma didn't want to let him leave.
"The player then thought he could leave in January or February with extremely small conditions for Roma.
"He told us: 'We will meet again soon.' I hope it is not over."