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Lukaku, who has scored 15 times this season, was stretchered off against Southampton on Saturday following a clash of heads with Wesley Hoedt.
That ruled Lukaku out of Monday’s trip to his former club Everton and he is set to be absent for the FA Cup third round tie with Derby on Friday.
Speaking prior to the Everton match, Mourinho told Sky Sports: “I would say a week (out for Lukaku).
“It’s nothing really important – just a little protection, but no problem.”
United’s next Premier League game, at home to Stoke, isn’t for 10 days after the Derby game, giving Lukaku time to return for that fixture.
Lukaku crashed into Southampton’s Wesley Hoedt on December 30 as the pair contested an aerial challenge early in the first half at Old Trafford.
The Belgium striker lay prone on the pitch barely moving while he was treated by medical staff for five minutes.
Lukaku remained conscious and was eventually carried off wearing an oxygen mask.
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