The Serie A champions had moved ahead of their domestic rivals after offering to send Paulo Dybala in the opposite direction.
However, the Argentina international's wage demands and lack of interest in a switch to Old Trafford scuppered that deal.
That has handed the initiative back to Inter, who have been tracking Lukaku ever since Antonio Conte was installed as their new manager at the end of May.
The Nerazzurri have not yet come close to meeting United's £80m valuation, but that could change as the start of the Serie A season approaches.
And according to ESPN, United will not seek to replace Lukaku should he depart, with youngster Mason Greenwood poised to take his place in the squad.
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