New Inter manager Antonio Conte has made it clear he wants Lukaku, 26, to be the main man in his attempts to end the Juventus domination of Serie A next season.
But SunSport understands United made it clear to the Italians they were not budging on the £75m they believe the Belgium star is worth.
Lukaku is currently out in Australia with the rest of Ole Gunnar Solskjaer's squad, an evening training session with a slight niggle - hours before the meeting took place at lunchtime UK time.
He has told Solskjaer he would rather make the switch to the San Siro this summer, having felt undermined by his treatment from the manager last season.
But Inter are struggling to come up with the money to meet United's asking price, and are hoping they can persuade Woodward to reduce his demands over the coming ten days.
It is believed they would be prepared to pay in the region of £65m for the striker, who United signed from Everton in a £75m deal two years ago.
Their preferred option, which would help with their FFP balance sheets, is effectively a hire purchase where they structure the transfer as a loan leading to a permanent move.
That would see them make a down payment around £15m, with a legal obligation to make the transfer permanent with two further payments taking the value up to £65m.
United are not keen on receiving the money over such a long period, and instead would prefer a far bigger down payment in a straight transfer, with smaller instalments to follow.
If Lukaku does move, it is belied United will have to pass on £5m to Everton under the terms of their transfer deal in 2017.
Inter have not given up hope they can strike a deal, and talks will continue over the coming days with United happy to listen to an offer.
The two clubs face each other in a pre-season friendly in Shanghai on July 20, and it could be the move might be concluded out in the Far East.
