Lukaku did not play any pre-season matches for United during the close season, and spent the last few days training with Anderlecht.
United seemingly prefer Marcus Rashford as their first-choice centre forward and as such Lukaku looks set to depart ahead of the new season starting.
25 - The most fruitful Premier League campaign of Lukaku's career came in 2016-17, when he scored 25 for Everton - the most in a single season by a Toffees player since Gary Lineker hit 30 in 1985-86.
However, sources have told ESPN FC that Luke Shaw, who was bottom of the list, was among those unhappy the information had been made public, prompting Solskjaer to rebuke the Belgian.
Arsenal were also reported to have agreed a fee with Celtic for Scotland full-back Kieran Tierney.
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Daniel James, Aaron Wan-Bissaka and Harry Maguire were the only incomings with some supporters feeling more signings were needed, particularly in midfield.
The clubs remain apart in their valuation of the striker, with United wanting to recoup at least the Sh9.4 billion (£75m) they paid Everton two years ago.
Wales coach Ryan Giggs says he can't blame Romelu Lukaku leaving Manchester United for Inter Milan.
Chelsea midfielder Danny Drinkwater, who has struggled to get game time in the two years at Stamford Bridge since his move from Leicester, joined Burnley on a six-month loan deal.
Milan-based Gazzetta Dello Sport reports that the player will earn €8.5 million a season at Inter, and claims that the club will pay United €65 million up front with a further 10 million in add-ons.
Lukaku's move marks the end of one of the summer window's longest-running transfer sagas.