The 20-time English champions have completed only one signing so far in this transfer window, that of Victor Lindelof. The Swedish defender arrived at Old Trafford from Benfica earlier in June.
According to the Guardian, the Red Devils manager is frustrated with the lack of transfer activity and wants two new faces added to the squad before they fly to the United States for the club's pre-season tour.
Mourinho has managed both Morata and Matic during his spells at the Spanish capital club and Stamford Bridge, respectively, and is keen to reunite with them at Old Trafford.
It was the Portuguese tactician who promoted the striker to the first team at Real, while he also re-signed the Serbian international at Chelsea in January 2014.
United's executive vice-chairman Ed Woodward flew to New Zealand to watch the British and the Irish Lions' first test against the All Blacks last week despite the on-going negotiations for the two players. Mourinho now wants Woodward to step up in order to complete both deals.
IBTimes UK earlier revealed that the Red Devils and Real had made significant progress in the negotiations for Morata after a major hurdle in talks were cleared last weekend.
The Spain international's father, Alfonso, and his agent, Juanma Lopez, were at the Santiago Bernabeu to discuss the striker's future and the deal is likely to be completed before this weekend.
Meanwhile, Chelsea are set to sanction Matic's sale to United only after they complete the signing of Tiemoue Bakayoko from AS Monaco. The France international is reportedly expected to join the Blues in the next 48 hours.
Mourinho prefers to have his new signings for the pre-season as it allows players to settle quickly at the club.
Last summer, United had completed the signings of Eric Bailly, Zlatan Ibrahimovic and Henrikh Mkhitaryan before the pre-season. Paul Pogba's deal, which was a protracted transfer saga of sorts, was completed in August.