PSG know they must replace Thomas Meunier, who is out of contract in June and could join Borussia Dortmund.
Another right-back on the books, Colin Dagba, 21, has not convinced leaders of the Parisian club.
PSG have launched a search for right-backs, with 22-year-old Baku one of those under consideration.
A Germany under-21 international, Baku is a converted midfielder who has flourished in his new right-back role.
Baku has two years left on his Mainz deal and his market value is between €5m and €8m.
On Sunday, he showed his talent against FC Köln, putting in an excellent performance and assisting Taiwo Awoniyi’s goal.