The 17-year-old made his first-team debut for Spurs earlier this season before earning his first senior international cap for Ireland last week.
Parrott set up the second goal in a 3-1 win for Mick McCarthy’s side over New Zealand in a friendly in Dublin.
They are monitoring his impressive development with an eye to making a bid, with his current contract due to expire in 2021.
Jadon Sancho’s success at Borussia Dortmund since joining the German club from Manchester City in 2017 has encouraged Bayern to monitor the English youth market more closely.
And Parrott’s scoring record at youth level is particularly impressive, with five goals to his name in three UEFA Youth League appearances this season.
He bagged 19 goals in 27 appearances between the club’s Under-18 and Under-23 last term.
Bayern have previously shown interest in young England-based talent with their pursuit of Chelsea’s Callum Hudson-Odoi, but the England winger eventually signed a new deal at Stamford Bridge.
Bayern recently sacked manager Niko Kovac after a mixed start to the season.
They are currently third in the Bundesliga standings, four points behind leaders Borussia Monchengladbach.
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