Lukaku has been fined two weeks' wages — in base salary terms about £230,000 — by United for missing training without permission this week as well as a controversial tweet last Friday in which he divulged confidential training data.
Lukaku, 26, angered Solskjaer by revealing the speeds run by United's squad during a training session in Perth on the first leg of United's pre-season tour. Lukaku felt his tweet was merely a response to critics who have accused him of lacking pace and fitness but he was ordered to delete it.
It led to a heated meeting between Solskjaer and Lukaku on Sunday in which the player felt he was told he had to work away from United's first team. Lukaku — who has missed all six of United's pre-season matches with what was officially cited as an ankle injury — ended up travelling to Belgium to train with his former club Anderlecht.
Although pictures of Lukaku training with Anderlecht on Monday bemused United officials, it was explained that the players were on a day off but that the Belgian would be expected back on Tuesday.
Yet Lukaku failed to report, spending another day at the Neerpede complex outside Brussels, and is understood to have remained in Belgium yesterday.
Lukaku's failure to report at Carrington is understood to have resulted in a fine although the player may opt to contest the punishment in the belief he did have permission to be away.
Lukaku earns a basic salary of £115,000 a week, albeit more than double that once bonuses and image rights are factored in.
Antonio Conte, the Inter coach who tried to bring Lukaku to Chelsea before United's late hijacking of the move in 2017, had feared he would miss out on the player again when United began negotiating with Juventus as part of a proposed swap deal with Paulo Dybala.
But that move collapsed over the weekend when United backed away due to reservations about Dybala's willingness to move to Old Trafford, his wage demands and agents' fees, thought to be in excess of £13 million, as well as complications over the Argentina striker's image rights.
That cleared the way for Inter to sign Lukaku but their failure to offload Mauro Icardi proved a complicating factor.
Whether United manage to bring in a replacement for Lukaku before the close of the Premier League transfer window today remains to be seen.
Solskjaer is thought to be comfortable with his squad and, determined the Lukaku saga does not overshadow preparations for the opening match against Chelsea at Old Trafford on Sunday, he has been happy for the Belgian to leave without a replacement.
The form of 17-year-old Mason Greenwood in pre-season has encouraged Solskjaer and he will ask Marcus Rashford and Anthony Martial to spearhead the attack.
Lukaku has struggled to win over Solskjaer, who wanted a more fluid attack able to press aggressively. Solskjaer has prioritised retaining another unsettled player in Paul Pogba but none of the France midfielder's suitors, including Real Madrid, have been able to meet United's £160m-plus valuation.
United, meanwhile, have rebuffed an approach from Everton to take defender Chris Smalling on a season-long loan.
- Telegraph Group Ltd
