Emerson was allowed to leave Stamford Bridge ahead of the 2021/2022 campaign, having fallen behind Ben Chilwell and Marcos Alonso in the pecking order.
However, with Chilwell ruled out until next season with an ACL injury, Thomas Tuchel is short of options at left wing-back.
Tuchel has now identified Emerson as his preferred replacement.
With no recall option included in the arrangement, Lyon are under no obligation to allow the Italian defender to return to Chelsea.
The Ligue 1 side also do not want to lose the 27-year-old who has been a regular in their starting lineup.
According to Italian journalist, Fabrizio Romano, that has resulted in the Premier League club offering Lyon a fee of €4m (£3.33m) to use their own player during the second half of the season.
Romano adds that Lyon have already rebuffed two approaches from Chelsea, although the European champions may persist with their efforts with Tuchel having recently spoken of his admiration of the player.