The 19-year-old arrived in Europe two years ago with Bayer splashing out €20m, a club-record sale for Vasco da Gama.
Paulinho has struggled to make an impact in the Bundesliga, rarely starting games over the past two seasons.
However, his potential was on show against Eintracht Frankfurt on March 7 when he scored two and assisted one.
TMW claims Bayer could be open to a sale, with the Brazilian teenager proposed to Milan and Roma in the last few weeks.
Ralf Rangnick has studied and rates the player, which could make Milan an option when the German arrives.
Meanwhile, Roma plan to sell Cengiz Under, Diego Perotti and possibly Justin Kluivert, so will need reinforcements.
Bayer have not set a price for Paulinho, but it would probably be less than the €20m they paid in 2018.