De Ligt was absent again as United beat Sabah 4-0 in their opening Champions League fixture in midweek, and the centre-back will also miss Sunday's Manchester derby against Manchester City.
The Netherlands international has not featured for United since sustaining the back injury last season, an issue that eventually required surgery over the summer and has kept him sidelined for the best part of a year, well beyond the club's original expectations for his recovery.
Manchester United went on to win just one of nine matches without him at the turn of the year, a difficult run that ultimately cost previous manager Ruben Amorim his job before Carrick was handed the role on a permanent basis.
Carrick, speaking ahead of the derby, said De Ligt's recovery is entering its final stage after a long and frustrating rehabilitation process for the defender, who has been a regular fixture at the club's Carrington training base throughout his absence.
"It looks positive," said Carrick. "Matthijs has trained really well, but we're managing his situation closely. When you've been out for such a long time, you reach that final phase where you have to work even harder, and you also need to get through that last stage properly."
The United boss said he is hopeful of having the 27-year-old back in contention soon, describing his continued presence around the squad as a boost.
"Matthijs is in a good place, and it's great to have him back around us again," Carrick said. "Hopefully he can return to action before too long."
United sit 11th in the Premier League after three matches, having lost to Hull City, beaten Ipswich Town and drawn with Everton, and De Ligt's return would provide a timely boost to Carrick's defensive options as the season progresses.
United's Champions League campaign continues later this month, with further fixtures against Atletico Madrid, Bayern Munich and Villarreal still to come in the league phase.
United signed the defender from Bayern Munich in the summer of 2024 for a fee of around €45 million, and the 2018 Golden Boy winner has made 56 appearances for the club to date.