The 20-year-old starred for Brescia last season despite them eventually being relegated from Serie A, and is regarded as one of the most exciting young Italian prospects playing at the moment.
Since the season ended, Inter have emerged as favourites to sign Tonali, with them putting together a loan move followed by the obligation to buy next summer for €31m.
Although they led the chasing pack, things went quiet slightly, which has led to others increasing their attempts to sign him.
According to Corriere Dello Sport, Manchester United have entered the race for his signature, with Ole Gunnar Solkskjaer seeing the young Italian as the perfect partner for Bruno Fernandes and Paul Pogba in the middle of midfield at Old Trafford.
However, another more likely suitor has emerged in the form of Milan, who have offered €10m upfront for a loan plus a further €25m to make the move permanent, which could present a more desired scenario for Brescia.
Tonali is also a boyhood Milan fan and Corriere della Sera report that he would be excited by the prospect of becoming a key element of Stefano Pioli's resurgent Rossoneri side.
Things have been quiet on the transfer front for Man Utd so far in this window, with them failing to make a single signing as of yet.
They were previously Interested in Jadon Sancho of Dortmund but the Bundesliga side are refusing to budge on their €112m valuation of the Englishman.