Zirkzee is on the books at German giants Bayern Munich, but the club are prepared to let him move on before the transfer window closes.
Everton have been holding talks with Bayern Munich in a bid to take the striker to Goodison Park, but have not reached an agreement yet, with the Toffees unwilling to agree to a purchase option in the loan deal which would be set at €10m.
Now Everton face competition for Zirkzee as, according to Sky Italia, Serie A club Parma are trying to sign him.
Parma are in deep trouble in Serie A, sitting in 19th, and scoring goals has been an issue for the club.
They have managed just 14 goals in 18 Serie A games and are keen to add to their attacking options, with Zirkzee fitting the bill.
The Dutchman has played for Bayern Munich in the Bundesliga this season, but most of his action has come with Bayern Munich II in the 3. Liga.
Zirkzee is under contract at Bayern Munich until the summer of 2023.