The Brazilian teenager has struggled for game-time since joining the club in the 2024/25 season, making only eight appearances in the starting line up under former Los Blancos boss Carlo Ancelotti.
However, the 19-year-old has yet to make an appearance this season under new head coach Xabi Alonso and needs to play regularly in order to make the Brazil squad for next years' global showpiece.
According to the Daily Mail, Lyon have offered a six-month loan deal with partial salary coverage as they look to strengthen their attack for the second half of the season.
Earlier this year, Endrick admitted to Romario TV about his concern of being left out of the 2026 World Cup squad due to lack of game-time.
"To tell you the truth, what goes through my head a lot is that I'm afraid I won't be in the World Cup," said the young forward.
"So, I have this fear. Because it's a dream of mine. It's hard to say because I want to be at the World Cup and help Brazil win its sixth title.
"Of course it's difficult, being at the biggest club in the world, with the biggest players, and you can't always have the opportunity to play."
Lyon are currently lying second on the Ligue 1 table, two points behind Paris Saint-Germain and are also competing in the Europa League this season under coach Paulo Fonseca.
Endrick has featured 14 times for the Brazil national team, scoring three goals.