كتب : Ahmad Saied
Ribery, who plays for Marseille, may be signed by the end of the week, added the sports daily in its unsourced report.
The 23-year-old told his club on Saturday that he doesn't want to stay despite committing his future to Marseille after the World Cup.
"I want to leave because I want to win things. I want to play in the Champions League," Ribery was quoted as saying by French media.
"I want to continue to develop; I want to be around big players. For me, that's important."
Ribery was linked with Premiership giants Arsenal and Manchester United but he is keen on joining Lyon, France's undisputed champions for the past five years.
But Marca said that Real Madrid are favorites to land Ribery after Marseille sports director Jose Anigo confirmed that his side will never sell Ribery's contract to Lyon.
Real boss Fabio Capello is reportedly searching for a talented winger after failing to acquire the services of either Chelsea's Arjen Robben or Arsenal's Jose Antonio Reyes.
Ribery played a wide role with France in the World Cup and was a starter in all the team's seven games till the final.