Lukaku did not play in any of United’s pre-season friendlies having been linked with a move away from Old Trafford.
Inter Milan and Juventus are both believed to be keen on the Belgian striker, who has gone AWOL from Manchester United.
He has been pictured training with Anderlecht though should have linked up with the Red Devils this week.
But he hasn’t appeared and Solskjaer has decided he will not be involved on Sunday as United begin their Premier League season against Chelsea.
Lukaku will also be fined for his absence with Solskjaer believed to be fuming with the former Everton man.
And Sky Sports transfer expert Kaveh Solhekol believes Lukaku will not return to Manchester until his future is resolved.
“It almost feels like Lukaku is defying Manchester United because he was told he had to return to training at United [on Tuesday] and he has not done that,” Solhekol told Sky Sports’ Transfer Talk.
“He is still in Belgium training with the Anderlecht youth side.
“From the outside looking in it looks like he is not following orders.
“Lukaku wants to stay in Belgium until there is clarity on his future.
“It just seems strange to me that a Manchester United player is not training with Manchester United.
“Even if United want to sell him and he wants to go to Inter Milan, surely it would suit him and United to be at Carrington doing what he is told.
“It is a bit of a worrying development if you are a United supporter.
“He seems to be defying orders almost. Why is he still in Belgium? He is a United player and he is still getting paid by United.”
Mason Greenwood is expected to be named in United’s squad with the young forward impressing in pre-season.
Marcus Rashford is likely to lead the line with Solskjaer favouring the England star over Lukaku.