According to The Sun's Jake Lambourne, Tonali's performances in Serie B have attracted the attention of Italian giants Juve, Inter, AC Milan and Roma, but Blues boss Maurizio Sarri has also kept an eye on him and has had him scouted.
Sarri's interest in him stretches back to his time as Napoli manager, and Chelsea could steal a march on their rivals by launching a significant bid for him in January.
The 18-year-old, who has been made a "top priority" by Chelsea, has contributed three assists in seven matches this season and is already drawing comparisons with Italy legend Andrea Pirlo.
Sarri's scouts watched him in a 4-1 win over Padova, where they will have seen him deliver two of those assists.
The coach is said to have been impressed with the youngster's maturity, and the player is "a composed playmaker with a sharp turn of pace," according to Lambourne.
Tonali helped Italy's under-19s reach the final of the UEFA European Championship this summer and was named in the team of the tournament:
The reported fee would nevertheless be an enormous amount to splash out on a player so young, particularly as he has no top-flight experience.
It's unlikely the other interested parties could risk that much on an untested youngster, even if he does have plenty of potential. If Chelsea are determined to land him, it's difficult to see Brescia turning down a bid of that size.