The powerful 24-year-old Belgian has netted 10 goals this season following his £75 million move from Everton.
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"He's humble, he wants to learn all the time, he wants to improve all the time," said Mourinho. "I think the ambition is there."
Mourinho said Lukaku's numbers this season were "amazing", attributing his success to his side's solid performances.
"It's a great achievement but it's only possible with a good team," said Mourinho. "And the team is solid, the team is playing well. We start the competitions strong."
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Lukaku, who signed a five-year contract with Manchester United in July, had rejected a new deal at Everton in March to reunite with Mourinho, under whom he played at Chelsea.
United, unbeaten this season and level on points with Manchester City at the top of the Premier League, lead Champions League Group A by three points after convincing wins over Basel and CSKA.
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