The former Bologna star has been linked with a return to Serie A, while West Ham United are also interested in the Dutchman.
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However, a move to Spain is also being raised, says the Mirror.
Sevilla are interested in Zirkzee, where after a slow start, the team is flying under new coach Matias Almeyda.
The Argentine is eager to increase his firepower in January and Zirkzee is viewed as a viable option.