Lukaku joined United this week for £75m, which could eventually rise to a world-record fee, from Everton, with Mourinho being the one who sold him to the Goodison Park club.
The Belgian was initially loaned out by Mourinho to the Toffees before selling him for £28m in 2014 with there being suggestions that he wasn’t full convinced by the striker at the time, before Lukaku eventually revealed it was his decision to move to Everton to further his career.
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United had previously chased Antoine Griezmann, Alvaro Morata and Andrea Belotti before eventually signing Lukaku, although the club insisted he was their “principal signing” when he joined.
And Mourinho said the history of the pair working together at Stamford Bridge means they will not have to build a new relationship and they can pick up from where they left off.
"It's quite a great experience the fact we worked together already for a few months," said Mourinho.
"During the time when I was at Chelsea and then United, and he was at Everton, our relationship was always very close, despite not working together.
"He's intelligent, he's polite, we kept the contact, the feeling, and now we are back together in different moments and I have no doubts it is going to work."
During the pair’s time at Chelsea, Lukaku was seen as the heir to Drogba’s throne, given his big physical presence, but that never materialised as he failed to be given an extended run in the first team.
But Mourinho refused to compare the two players, insisting all he is looking for from the 24-year-old is goals.
“I don't compare, I don't compare at all,” he said. “One has his history and one is still in the beginning of his history.
“What he brings is hopefully goals. He's the kind of player that everybody knows he's a striker, so we're not speaking about a multi-functional player or one where there are doubts about his position on the pitch.
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“He's a striker and normally strikers score goals and the reason why he was so important and difficult to get is what he did in the Premier League.
“He has played in the Premier League for the last four or five seasons, so now he comes to a club with a different responsibility than Everton or West Brom.”
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