United have already signed Brazil midfielder Fred from Shakhtar Donetsk in deal worth in the region of £52m and Porto right-back Diogo Dalot for a fee of £19m.
Goalkeeper Lee Grant has also moved to Old Trafford and has impressed in United’s first two pre-season games in America.
But with little more than a fortnight left to go until the transfer window slams shut, Mourinho has made clear he is eager to bring in more players.
“One thing is what I would like,” he told ESPN FC. “Another thing is what is going to happen.”
Asked directly how many new signings he would like, Mourinho said: “I would get two more players.”
But Mourinho indicated a right-back is not currently on his agenda, despite injuries to club captain Antonio Valencia and teenager Dalot.
Valencia lasted just seven minutes of United’s goalless draw with San Jose Earthquakes at the weekend before being withdrawn due to a suspected calf injury, which appears to have ruled him out of the remainder of United’s American tour.
Matteo Darmian, who replaced Valencia in the friendly, has been linked with a move away from Old Trafford, and his departure would further reduce Mourinho’s options at right-back.
“I don’t think he will be available to play any one of the three matches of the International Champions Cup,” Mourinho said.
“It’s not a moment to take any risks. Antonio is a player that’s not a young boy anymore. We have to take care of him and to try to have him ready for the start of the season.
“We bought a fantastic player [Diego Dalot]. Young, 19 years old, but I think probably the best right-back at that age in European football.
“But he had a surgery last May and is recovering for that, so one more reason to take care of Antonio.”