The Belgium international has been heavily linked with a summer switch to Inter Milan, but a deal is yet to be struck and United are continuing to demand £75 million for the striker.
According to The Sun, manager Ole Gunnar Solskjaer vowed to the 26-year-old that he will be given the opportunity to make the No.9 position his own in 2019/20 if he stays put.
The plea was made during a conversation before the squad flew to Australia to begin their pre-season tour on Sunday.
Lukaku faces competition for a starting striker role from Marcus Rashford, who signed a new contract with the Old Trafford club this summer.
The report adds that Juventus and Napoli have also shown interest in the former Everton man after he lost his place in the team last season.
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