Carrick hung up his boots at the end of last season after a 12-year playing career at Old Trafford, with the midfielder immediately promoted to a role on Mourinho's coaching staff.
Manchester United's preseason is underway.
"It is not about when he can [play], but when he has to", Mourinho told a news conference on Thursday following the 1-1 draw with Club America in Phoenix.
The Chilean returned to pre-season training at Manchester United's AON Training complex, but was forced to stay behind in the UK as the side departed for the US last Sunday.
The Red Devils are now training in California as they prepare for their first pre-season match on Friday, against Club America at the University of Phoenix stadium in Glendale.
United started the game with a back four of Antonio Valencia, Eric Bailly, Chris Smalling and Luke Shaw. Subs: J Pereira, Darmian, Fosu-Mensah, Tuanzebe, Williams, Hamilton, Garner, Gomes, Chong, Bohui, Greenwood.
"But I never cared much about the captaincy, I care more about the life in the dressing-room and the leaders".
Manchester United and Jose Mourinho will be looking to get some deals over the line before the transfer windows slams shut on August 9.
The Premier League side were without many key players after the World Cup.
It became apparent the problem related to not being granted a visa as a result of accepting a 16-month suspended jail sentence in Spain earlier in 2018 for tax fraud.
Demetri Mitchell, impressive on loan at Hearts last season, threatened on the left wing and Anthony Martial, starting as the centre-forward, fired over and then forced America goalkeeper Agustin Marchesin into a diving save.
There were opportunities for both sides during a goalless first half, with Mata going closest for United, hitting the right-hand post from 15 yards with a low, left-footed effort through a crowded box.
"There's no Lukaku or Rashford - not here, and probably not even for the start of the Premier League".
The Chilean was not with José Mourinho's squad when it flew to Los Angeles on Sunday as he was not granted a visa by the USA authorities.