Manchester United boss Solskjaer could lose Lukaku to Inter Milan, with the Serie A giants keen to lure the Belgium international to the San Siro.
The former Everton star has been told he will play second fiddle to Marcus Rashford in attack next season and, consequently, is keen to make the move to Italy.
Manchester United have so far held firm, though, with the Red Devils holding out for £90million in order to let the striker go.
Inter are financially strong but even they have doubts as to whether or not Lukaku is worth a punt for that price.
And the Times say that, if Lukaku goes, Solskjaer is adamant that Woodward must fork out on a replacement.
United, when it comes to strikers, have several player capable of operating in a No 9 role.
Rashford can play there, while Solskjaer has trialled using Anthony Martial in a central position.
Alexis Sanchez, who is expected to stay at the club amid United’s failure to find a buyer, had the best season of his career when playing as a striker for Arsenal.
And teenage prodigy Mason Greenwood has made a name for himself at academy level operating at the tip of the attack.
Man Utd boss Ole Gunnar Solskjaer is relying on Ed Woodward for transfers (Image: GETTY)
Man Utd boss Ole Gunnar Solskjaer is adamant he will need a Romelu Lukaku replacement (Image: GETTY)
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