Lukaku signed for Manchester United in 2017 for a huge £76m but only stayed at the club for two years.
Steve Walsh was Everton's director of football at the time of the transfer and he was concerned by the Belgian's attitude.
Walsh played a key role in Leicester City's title-winning season of 2015/16, when he was a scout for the Foxes.
Jose Mourinho had an existing relationship with Walsh, having worked with him during his first stint at Chelsea.
And Walsh made sure to warn his former colleague of Lukaku's allegedly poor behaviour.
"When Jose [Mourinho] signed Romelu Lukaku from Everton, I remember saying to him, 'You have to be careful with Lukaku. He is a big baby, you know'," Walsh told The Athletic.
"He said he could handle him. I don't think he really got Lukaku on-side mentally, which you have to do.
"That is the case with him and Paul Pogba. They aren't my type of players. They are more about themselves than the team. I wouldn't have touched them.
"Because they are good players doesn't mean you are going to get a good team out of it."
Everton sacked Walsh in 2018 and he was replaced by Marcel Brands.
Mourinho also got the sack 18 months after signing Lukaku and the striker followed his former manager out of the club last summer when he signed for Inter Milan.
Lukaku has found form in Italy under Antonio Conte, with whom he shares an apparently special relationship.
He's managed nine goals in 15 games this so far this season.
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