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United's England contingent Wayne Rooney, Chris Smalling and Marcus Rashford will be on the tour.
However, Mourinho has said the trio will not play against Borussia Dortmund in Shanghai on 22 July and Manchester City in Beijing on 25 July.
And new signing Ibrahimovic, 34, may not be involved at all.
If he does not go to Asia, it is not known precisely when Ibrahimovic will make his first United appearance.
The striker, who arrived at United on a free transfer after his contract with Paris St-Germain expired, last played in Sweden's final match at Euro 2016, a 1-0 defeat by Belgium on 22 June.
When it was confirmed on Monday a United XI would play Salford City at Moor Lane on 26 July, the National League North club's co-owner Gary Neville said on Twitter: "Zlatan first game!!"
United's first team play Galatasaray in Gothenburg in Ibrahimovic's native country on 30 July.
They play Everton in Wayne Rooney's testimonial at Old Trafford on 3 August and Premier League champions Leicester City in the Community Shield on 7 August.