Zirkzee impressed while on loan in Belgium at Anderlecht last term, but is down the pecking order of attackers at Bayern Munich and is expected to be moved on.
He has interest from the Premier League where Fulham, Southampton and Bournemouth are all fans of what he brings to the table.
Fulham have already opened talks with Bayern Munich to try to agree a deal for Zirkzee and it remains to be seen if Southampton and Bournemouth follow suit.
The trio could have competition from the Bundesliga though.
Stuttgart are also admirers of Zirkzee and if they lose the services of striker Sasa Kalajdzic, they will launch a bid to snap him up.
He made 47 appearances for Anderlecht last term during the course of his spell in Belgium and scored 18 times, along with providing 13 assists.
It remains to be seen where Zirkzee, 21, is playing his football when the transfer window shuts on 1st September.