The Dutchman has struggled since his summer arrival at United from Bologna.
And La Repubblica says Juve are keen to explore a loan arrangement for the striker in January.
Zirkzee enjoyed great success with Bologna under current Juve coach Thiago Motta, who is keen on a reunion.
And it's suggested new United manager Ruben Amorim is willing to sanction his departure, as he's unconvinced by the young forward's place in his system.