The Dutchman is attracting plenty of interest after enjoying a productive campaign in his second season as a Bologna player.
Zirkzee scored 11 goals and provided five assists in 34 appearances to help Bologna achieve Champions League qualification in the 2023-24 season.
The Italian side have already seen manager Thiago Motta leave for Juventus, and they are now facing a battle to keep hold of some of their key players, including their star striker Zirkzee.
Zirkzee is said to have a €40m (£33.9m) release clause in his Bologna contract which is only valid until the middle of August.
Premier League duo handed boost in Zirkzee pursuit
Premier League giants Man United and Arsenal have both emerged as potential suitors for the Netherlands international.
The two English clubs have now received a boost in their respective pursuits after Bologna director Giovanni Sartori admitted that Zirkzee will almost certainly leave this summer.
"Zirkzee has a release clause into his contract and I believe he's 99 per cent gonna leave the club," Sartori said at the opening of the Serie A transfer market.
Man United and Arsenal may be encouraged by Sartori's remarks, but they could still face competition from Italian giants AC Milan.
The Rossoneri are currently refusing to pay the €15m (£12.7m) commission demanded by Zirkzee's agent despite agreeing personal terms with the Dutch forward.
Why are Man United and Arsenal targeting Zirkzee?
Man United currently have Rasmus Hojlund as their main centre-forward option following the departure of French striker Anthony Martial.
Although Marcus Rashford can play as a number nine, the Red Devils are keen to recruit a new marksman ahead of the 2024-25 season.
Meanwhile, the Gunners are also looking to strengthen their forward options this summer, especially as Eddie Nketiah could be sold following a lack of playing time last term.
If Nketiah were to depart, Arsenal boss Mikel Arteta would be left with Kai Havertz and Gabriel Jesus as his two senior centre-forwards.