The Nerazzurri have been pursuing 20-year-old Tonali for months as part of plans to change the midfield.
And they have reportedly reached an understanding with relegated Brescia to take Tonali on loan with an obligation to buy.
The clubs are still settling the figures, but negotiations are so advanced that Tonali has cut short his holiday.
Tonali, already a three-time Italy international, will pen a five-year deal with Inter once everything is sorted.
In total, including loan fees, the operation will be worth in the region of €35m.
However, Conte’s future is in doubt after Inter’s Europa League final defeat to Sevilla, with a meeting planned.
Former Juventus boss Max Allegri is the hot favourite to take over if Conte goes, and may have his own ideas