The responsibility was held by Michael Carrick, who retired from playing at the end of last term and joined United’s coaching team.
Carrick made only five appearances in 2017-18 and Valencia wore the captain’s armband on numerous occasions.
The 32-year-old full-back skippered the team in the 1-1 friendly draw with Club America in Arizona.
Mourinho said afterwards: “The captain was Valencia last season. I think he is going to be the captain.
“And when he doesn’t play, we have to make decisions – it depends who is on the pitch. If (Chris) Smalling is, or if Ashley Young is, or if (Ander) Herrera is, or if (Juan) Mata is, if they are on the pitch, they are an option.
“I think a guy like (Nemanja) Matic has all the attributes to be Manchester United captain but of course he arrived only one year ago.
“But for me, I don’t care too much about the captaincy, I care more about the life in the dressing room and the leaders in the dressing room.”
The pair, who got to the semi-finals of the World Cup with Belgium and England respectively, are not on United’s pre-season tour as they take a post-tournament break.
Fellow forward Alexis Sanchez has been given the green light to join up with the squad in the United States.
Sanchez had initially been left in Manchester due to what the club said was a “personal administrative issue” – widely assumed to be a problem with his visa after he accepted a 16-month suspended prison sentence in Spain earlier this year over a tax issue.
Mourinho said in a press conference shown on Sky Sports News: “Today it was (Anthony) Martial. When Martial left the pitch, it was Mata (leading the attack). When Mata went to the sides, it was a kid that trained with us for the first time this pre-season (Mason Greenwood).
“There’s no Lukaku or Rashford – not 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 because he trained with us for five days before we departed to Los Angeles (on Sunday) and we left one fitness coach behind with him to keep training with him.
“Of course, it’s individual training but when he arrives, he has to play.”
Paul Pogba, Marouane Fellaini, Jesse Lingard, Ashley Young and Phil Jones were other United players involved in the World Cup’s last four.
United’s next match of the tour is against San Jose Earthquakes on Sunday in California.
Their opening Premier League fixture is on August 10 against Leicester at home.
Jose Mourinho doesn’t believe Tahith Chong belongs in the Manchester United first team yet, but has plans for the teenager to train more with the senior side in the hope of “increasing his evolution”.
Mourinho feels Chong, 18, is good enough “technically and tactically” to play for United but is not yet there physically as he heaped praise on the Dutch winger following his involvement in the equaliser as the Red Devils came from behind to draw 1-1 with Club America in Phoenix in their opening pre-season game on Thursday.
The Portuguese is without a host of his World Cup players in the United States as Paul Pogba, Romelu Lukaku, Marouane Fellaini, Marcus Rashford, Jesse Lingard, Marcos Rojo, Phil Jones, Victor Lindelof and Ashley Young enjoy a break after their extended exploits in Russia, with David De Gea, Nemanja Matic, new signing Fred and Alexis Sanchez set to join the squad in the next few days.
“I have plans to make him train the most possible times with us, because that increases his evolution,” Mourinho said of Chong.
“But he has to play where he belongs, he has to play in the academy and develop physically, because physically is where he’s not ready.
“Technically, he’s very good, tactically he understands the game and he understands his position, but by the physical point of view, when the game gets into contact situations, he’s in trouble, he’s fragile, he’s still a kid.
“But the talent is there, the personality is there, the passion to play, the humility to learn, so this is a fantastic experience for him. It depends on some cup matches. He’s one of the good kids we have, but it’s not for today but for the tomorrow – he’s a good kid.”
United start their Premier League campaign against Leicester on August 10.
Chong joined the Premier League side from Feyenoord in 2016 and has been part of the Under-18 side since.
He recently overcame a cruciate ligament injury and is continuing to impress. He replaced Anthony Martial after an hour in front of a sparse crowd of 37,660 that was markedly below the University of Phoenix Stadium’s 63,400 capacity.
Chong’s debut for the first-team was followed by Mason Greenwood – two years his junior – when he came on for the impressive Luke Shaw with 14 minutes remaining.
Chong played his part in Juan Mata’s equaliser 12 minutes from time when he fired in a cross which Ander Herrera headed against the right post and Mata scrambled home.
Although Mourinho sees physical limitations in the youngster, who was young player of the year at United last season, the manager praised him for his confidence.
Mourinho added: “He was good. He came with the intention to show, and in a moment where we have no strikers on the pitch, Martial was the only one and then he left, so we needed people to create, have some initiative, which he did.
“The action for the cross for the goal is a beautiful action. He was enthusiastic, he was confident to play.
“Of course physically he has his limitations, and when he has one more touch and he allows that body contact of course he loses it, but when he makes the ball move and attacks people one against one, he has quality.”
Jose Mourinho expected Club America to put his new-look Manchester United squad through their paces – and his prediction appeared to be realised in the 1-1 friendly.
Missing star talents Paul Pogba and Alexis Sanchez, the opening match of a pre-season US tour looked like it might end in defeat for the Reds in Arizona until Juan Mata volleyed to equalise in the 78th minute.
Mourinho told MUTV: “After five days of training you need to play and it’s good to play against a team that is at three days’ distance from starting their Mexican league.
“So (they were) a team with with intensity, a team with quality that pushed us to levels that we are not prepared for… so a good training session.”
A goal-less first half at the University of Phoenix Stadium saw new signing Lee Grant make two saves, while United appeared to struggle to zero-in at the other end.
Anthony Martial and Mata came close, although none caused Club America stopper Agustin Marchesin too much strife.
Mourinho made two changes at the break, replacing Grant with Joel Pereira and switching captain Antonio Valencia for Timothy Fosu-Mensah.
Club America got the better of United in the 59th, Henry Martin finding the net with a stunning header off a cross by Antonio Lopez.
Luke Shaw made a follow-up attempt after play resumed, going wide to the right, and United went more than 15 minutes before another opportunity arose.
It looked to be another miss, Ander Herrera striking the left post with a header, but Mata was waiting at the side of the box to power the volley home.
United’s next stop is in California, where they will play San Jose Earthquakes on Sunday.
Pogba is having a post-World Cup break and Sanchez did not fly out with United at the weekend because of what the club said was a “personal administrative issue”.
New signing Fred, along with Sanchez, is expected to join the squad next week.