Dier, 22, has been watched by Bayern scouts in recent weeks, it is claimed, and were particularly impressed with his performance for England against Germany.
The Spurs ace scored the winner in the 3-2 friendly win last month, with Dier successfully shutting down playmaker Mesut Ozil.
Dier can play in both midfield and defence, and it is reported by BILD that he would replace 34-year-old Xabi Alonso, formerly of Liverpool and Real Madrid.
Bayern are set to lose boss Pep Guardiola at the end of this current season, with Carlo Ancelotti already announced as his replacement.
Interest from a club like Bayern would surely be flattering for Dier, and it is a sign of the significant progress he has made since joining Spurs two years ago.
Tottenham however have Dier tied down to an extended contract, with the England star signing a new deal last September to last him until 2020, SkySports reported.
Dier is a popular member of the Spurs squad, and has a strong friendship and midfield partnership with Dele Alli, and with Champions League football to play at the club next season surely, it is hard to see him walking away, even for Bayern.