The 23-year-old cost Milan in the region of €35m to sign from Flamengo, but has failed to impress.
Paqueta has appeared in 44 games for Milan, scoring one and assisting three goals.
He remains a promising talent and has been capped 11 times by the Brazilian national team.
But with Sandro Tonali joining from Brescia and another central midfielder lined up, Milan want to balance the books.
Nothing is advanced yet, but there is serious interest from Lyon for Paqueta, who Milan value between €20m and €25m.
The Bundesliga side are reportedly willing to pay €8m for the Bosnian international, who they have been trailing since August.