The Red Devils have made a blistering start to the 2016/17 Premier League campaign after back-to-back victories over Bournemouth and Southampton.
United were 2-0 winners against the Saints on Friday night thanks to goals from Zlatan Ibrahimovic either side of half-time.
Mourinho has signed Villarreal defender Eric Bailly, Swedish striker Ibrahimovic, Borussia Dortmund midfielder Henrikh Mkhitaryan and Juventus midfielder Paul Pogba in the summer transfer window thus far.
Former United midfielder Giggs, who won 13 Premier League titles during his decorated career under Sir Alex Ferguson, believes Mourinho will have a hard time keeping all the members of his Red Devils squad happy.
“The biggest problem Jose’s got is keeping everyone happy,” Giggs told Sky Sports after Friday night’s 2-0 win.
United will play in the Premier League, the Europa League, the League Cup and the FA Cup this season after Louis van Gaal failed to guide the Red Devils back into the Champions League last term.
The 20-time English champions will make the short trip to Hull City in the Premier League next weekend.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news