Wagner came up through Bayern Munich's academy, but departed for MSV Duisburg in 2008 after being unable to break through to the first team.
After playing for four more teams, Wagner joined Hoffenheim prior to last season and has been a hit for Nagelsmann's side, scoring 11 goals last season as Hoffenheim finished fourth in the Bundesliga, earning a surprise berth in the Champions League.
The 29-year-old made his debut for the Germany national team this season, and now has his sights set on a move back to his hometown club.
"There is nothing to announce besides that there is interest," Nagelsmann said Thursday at a press conference.
"Everyone knows that Sandro has kids near Munich, that Bayern is his youth club and that he isn't the youngest anymore. I am not angry about him."
Bayern striker Robert Lewandowski has urged his side to sign a back-up striker to help him shoulder the goalscoring burden, and it appears Bayern may turn to Wagner to fill that role.
Speaking to Goal, former Bayern striker Giovane Elber said Wagner would be a good option for the Bavarians.
"Bayern is a good club and Sandro Wagner knows the club. So I think it would not be a problem if he joins Bayern," Elber said.
"If you have the possibility to play for Bayern Munich, you don't think about it for a long time. As a player you know what a club Bayern are.
"Furthermore, Wagner is a German international, he would fit well for Bayern."