Tonali, 19, is considered one of Italy’s hottest prospects after playing a starring role in the club’s successful promotion bid last season.
The midfielder made his debut for the senior Italian national team in October 2019 and has made 18 league appearances so far, scoring one and assisting two.
Juventus and Paris-Saint Germain have also been credited with an interest in the youngster whose contract is set to expire in 2021.
Any potential move for Tonali would have to wait until the summer and despite his potential, it would be a massive risk given the transfer fee Brescia would demand.
Elsewhere, reports suggest Lille midfielder Boubakary Soumare has held talks with United over a move this month.
They claim the midfielder will decide between signing for United or moving to Chelsea before the deadline on January 31.
Soumare is under contract until 2022 and has made 18 league appearances this season.