The Red Devils were the closest challengers to champions Manchester City last season, but still finished 19 points adrift of their record-breaking rivals.
Mourinho, in his third campaign at the helm, is under pressure to bridge that gap and put United back in contention for domestic supremacy.
He has bolstered his ranks this summer with the additions of Fred, Diogo Dalot and Lee Grant, while talking up the expected impact of January arrival Alexis Sanchez in his first full season at Old Trafford.
Mourinho is, however, reluctant to be drawn on the chances of his side capturing a first top-flight crown since Sir Alex Ferguson slipped into retirement back in 2013.
Asked whether the Red Devils can be considered serious challengers ahead of an International Champions Cup clash with AC Milan, the Portuguese said: “I don't answer to your question.”
Mourinho has admitted that he would like to add at least two more fresh faces to his ranks this summer before the transfer deadline passes.
For now, though, his focus is locked on readying his side the best he can for the challenges which lie ahead.
He has had to work with depleted ranks in America as a result of World Cup stars taking much-needed breaks on the back of their efforts in Russia.
United are preparing to welcome the likes of Nemanja Matic, Fred and David de Gea back onto their squad, while Marcos Rojo could follow suit, but Mourinho is not happy with how his preparations have gone so far.
He said: "I have got good facilities, as always.
"I have got incredible commitment of the people that are involved with the process of preparing a good pre-season.
"I am happy with the matches, the evolution of the matches, but I don't have the players to work.
"I don't have the majority of the players that are going to be in the squad on the 9th of August, when the (transfer) market closes and we can make the squad official for the season.
"Of course I am not happy."
They return to Europe to face Bayern Munich before opening the new Premier League season at home to Leicester in August 10.