Antonio Conte is determined to land the Belgium international having made him a leading transfer target after taking charge at San Siro last month.
And having failed with a two-year loan plus obligation to buy offer, Inter have now proposed a deal of £60m plus bonuses.
The Nerazzurri are keen to wrap up a deal as soon as possible to allow United time to secure a replacement.
However, the Red Devils have already told the Italian outfit that they will not sell Lukaku for less than £79m.
The former Everton centre-forward scored 15 goals in 45 appearances for United last term.
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