The 19-year-old striker was in the squad for the Champions League final last season and is considered a highly-rated talent in the Netherlands.
However, Zirkzee has found minutes hard to come by for the Champions League winners this season, with most of his action coming for the club’s second string side in the 3. Liga and only three appearances in the Bundesliga.
Club Brugge have been tracking his progress, while Eintracht Frankfurt were lining up a move before a red card for the player led to doubts.
Everton have been claimed to be set to sign him, but according to Dutch magazine Voetbal International, they are still just weighing up a bid.
Toffees director of football Marcel Brands has been watching the young forward and is considering taking him to Merseyside this month.
Zirkzee is happy at Bayern Munich, but is open to a move away from the club as he wants to play more minutes in the first team.
Everton are believed to be considering signing him on loan with a view to a permanent deal in the summer.