The Sweden striker could be Mourinho's first signing - but who else could be coming through the doors of Old Trafford next season?
We want you to select your starting XI from the current squad and the many players United have been linked with.
United are likely to be busy in the transfer window as Mourinho looks to overhaul Louis van Gaal's squad to create a team of title contenders.
But how will that squad look come the first day of the season?
Will Mourinho splash the cash? Will he give youth a chance? Or will there be a full-scale clearout?
Who will be in the team for the start of the season? We've included the current squad plus a selection of players linked with United.
The defence was one area Van Gaal never managed to properly address.  A centre-half is needed and plenty of names keep popping up.
Real Madrid's young France international Raphael Varane could link up with his old boss, Everton's John Stones was denied a chance to work with Mourinho at Chelsea while Zenit Saint Petersburg's Ezequiel Garay has been linked with a move to United since the days of David Moyes.
Revamping the midfield could cost United millions. Cristiano Ronaldo, Gareth Bale, and the possible return of Paul Pogba would come with a hefty price tag.
Then there is Portugal and Sporting Lisbon's Joao Mario, who can play on the wing or in central midfield, Sevilla's Polish defensive midfielder Grzegorz Krychowiak and Arsenal target William Carvalho, another defensive midfielder, also from Sporting Lisbon.
United need goals and their attack will surely be addressed by the former Chelsea and Real Madrid boss.
Atletico Madrid's France forward Antoine Griezmann, Real Madrid's Colombian playmaker James Rodriguez and Napoli's Argentinean striker Gonzalo Higuain, who broke the Serie A scoring record last season, could all join Anthony Martial and Marcus Rashford at Old Trafford.
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Jose Mourinho has been named as the new manager of Manchester United - and it looks like he may bring Zlatan Ibrahimovic with him.