The move, which will see Lukaku join Chelsea for a second time, is unlikely to involve any players moving in the opposite direction. Marcos Alonso had been linked with a move to Inter as part of the deal.
Details are yet to be finalised in terms of a payment plan, but personal terms are not thought to be an issue. Sources have told ESPN that Lukaku's salary is in the region of £250,000 a week.
Sources at Inter told ESPN they never had any intention of Lukaku leaving, even rejecting an offer of €100m plus Alonso. It was only when Lukaku informed them of his desire to leave that the club decided they would evaluate any "unrefusable" offers.
Lukaku, 28, scored 47 goals in 72 Serie A appearances for Inter since arriving from Manchester United in an €80m deal in 2019.
The Belgium international began his career at Anderlecht before first moving to Chelsea in 2011, where he enjoyed loan spells at West Bromwich Albion and Everton. Lukaku then signed permanently at Everton and later moved to Old Trafford in 2017.
Andrew Cesare Richardson contributed to this report.