Tuttosport says Juve sports director Cristiano Giuntoli has been encouraged by United to take Rashford off their hands in January.
Juve can sign the striker for €50m cash, though United would also be open to an initial six-month loan for a fee of €3-4m.
Giuntoli is interested, though both he and coach Thiago Motta would prefer United teammate Josh Zirkzee.
Along with Zirkzee, Juve are also eyeing Napoli attacker Giacomo Raspadori and PSG centre-forward Randal Kolo Muani.