"There's no [Romelu] Lukaku or [Marcus] Rashford here and probably not even for the start of the Premier League, so it's about when Alexis lands and when he lands, he has to play", Mourinho said.
Alderweireld fell out of favour in north London last season and was replaced by Davinson Sanchez in Mauricio Pochettino's starting XI.
United finished 2nd in the Premier League last season but fell 19 points short of Champions and local rivals Manchester City, ultimately ending the year trophyless.
Manchester United have jetted out to Los Angeles to continue their pre-season preparations, but have had to do so without 15 first team players thanks to their involvement in the World Cup, a number of injuries, and Alexis Sanchez's difficulty in obtaining a USA visa.
José Mourinho had an array of options to choose from when selecting his new club captain, with many fans hoping Paul Pogba would be awarded the armband after the midfielder displayed his leadership skills in the World Cup for France.
Mourinho added: "He was good".
"Don't rule out a statement signing too, United - having opted not to pursue re-signing Cristiano Ronaldo nine years after he left the club for Spain - would surely be near the front of the queue if Gareth Bale also decides to leave Real Madrid this summer".
The winger, signed from Feyenoord in 2016, came on for the final 30 minutes at the University of Phoenix Stadium, but it was enough to make an impression on Mourinho.
"I was very focused on this tournament", Alderweireld said. "But he has to play where he belongs, he has to play in the academy and develop physically because physically is where he is not ready. He's a good kid".