The 20-year-old put in an impressive performance by scoring twice in a 9-1 win for the Azzurri in Palermo.
The Red Devils have held talks with Roma about Chris Smalling, who is on loan with the Serie A club for the 2019/20 season.
Roma are understood to be keen on making the centre-back’s move to the Italian capital permanent, and negotiations could lead them to the possibility of a move for Zaniolo.
The youngster is one of the most highly-rated young players in Serie A, after bursting onto the scene last season following his summer move from Inter Milan.
He is unlikely to go cheaply, but fits the profile of young talent around which Ole Gunnar Solskjaer is trying to build his side at Old Trafford.
The Italy international has scored five goals in 16 games for the Giallorossi in all competitions this season.
He recently hit a rich vein of form, finding the net in three consecutive league games to help push Paolo Fonseca’s side into sixth place despite a crippling injury crisis.
The Giallorossi return to domestic action on Sunday with the visit of rock-bottom Brescia to the Stadio Olimpico.
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