Bayern's hierarchy reportedly view the 30-year-old as a long-term managerial prospect and the Bundesliga champions could ramp up their interest following the dismissal of Ancelotti on Thursday.
Nagelsmann has won widespread admirers since taking charge of Hoffenheim in February 2016, steering the club clear of relegation two seasons ago and defying expectations to achieve European qualification last term.
Thank You for everything @MrAncelotti— Robert Lewandowski (@lewy_official) September 28, 2017
But while he has previously spoken of his affinity to "home" city Munich, Nagelsmann is playing down links to Bayern.
"My media department has kept everything away from me."Hoffenheim have won four of their six league matches this season to sit second, one point ahead of Bayern.