The Holland international has been linked with AC Milan, Manchester United and Arsenal. While Zirkzee's deal carries a buyout clause, it only applies to former club Bayern Munich.
Bologna chief Marco di Vaio says: "It only applies to Bayern, detailed. For the other clubs the price is open..."
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Bayern can buy back Zirkzee from Bologna for 40m.
However, the young striker has intimated a willingness to remain in Serie A next season.