Pavard will move to the defending Bundesliga champions once the 2018-19 campaign concludes, with the France international reportedly earning Stuttgart €35m. Atletico Madrid defender Hernandez is also a confirmed target for Bayern.
"We are very good friends and I think it would be fantastic if Lucas also came to Bayern," Pavard told Sport Bild.
"He proved that he is a great player. First, [we were] together for France, then for Bayern?
"That would make me proud, but it's a matter between Bayern and Lucas."