Carrick is not expected to be a regular starter next season, however, meaning that Mourinho will likely pass the captaincy around his squad, with Ander Herrera and Paul Pogba the frontrunners to receive the honour.
"We don't have a vice-captain, a captain is enough," he is quoted as saying by the Manchester Evening News. "Michael is obviously the captain and when Michael is not on the pitch somebody will take the armband but Michael is still the captain.
"I don't like a lot the criteria of the captain to be the player with more time in the club because sometimes you have somebody with the armband that doesn't have the qualities to be the captain and is just the captain because he arrived before other players.
"So we are going to try and feel, and make decisions, like [Antonio] Valencia, like Herrera, Paul, Ashley Young, [Chris] Smalling, we have people that step by step we have to prepare because Michael will be the captain for one year, maybe two if he decides to do that, and his body resists to the demands of the Premier League and the Champions League. But for the season only one captain."
United kicked off their 2017-18 pre-season campaign with a comfortable 5-2 win over Los Angeles Galaxy at the Stubhub Center in the early hours of Sunday morning.