The England international succeeded Ashley Young as the Red Devils' captain in January 2020, being bestowed with the armband by Ole Gunnar Solskjaer.
However, Maguire's fortunes have taken a nosedive under Ten Hag, who quickly demoted his skipper to a bit-part role for the 2022-23 season amid fierce criticism of his displays.
Raphael Varane, Lisandro Martinez, Victor Lindelof and Luke Shaw were all preferred to Maguire at the back, and Bruno Fernandes would normally wear the armband in his absence.
Nevertheless, the former Leicester City man retained his status as captain throughout the 2022-23 season, but an exit this summer has been strongly mooted given his lack of minutes.
England boss Gareth Southgate has continued to select Maguire amid his undesirable club situation, but the Three Lions manager has warned the defender that his spot could come under threat if his playing time does not improve ahead of Euro 2024.
West Ham United, Newcastle United and Tottenham Hotspur have all been linked with moves, but it has been suggested that Maguire is keen to stay and fight for his place at Old Trafford, where he is under contract until 2025.
However, The Sun reports that Maguire will soon lose the armband regardless of the outcome of the transfer saga, and Ten Hag will soon meet with his squad to get their views on the matter.
The report adds that Fernandes is seen as the most likely to earn the captaincy on a permanent basis, despite questions surrounding his suitability for the role last season.
Any possible exit routes for Maguire are also said to be complicated by a recent pay rise, which was awarded to the entire Man United squad for their qualification for their Champions League.
The centre-back is said to earn in the region of £200,000 per week at Old Trafford, and the Red Devils could also be forced to hand him a payoff to negate any lost monies if a buyer is found.
Man United forked out a whopping £74.3m to prise Maguire away from Leicester in 2019, and the Englishman has since produced seven goals and five assists in 175 matches for the club.
However, Maguire started just eight Premier League games last season and played a combined two minutes in their EFL Cup and FA Cup finals, coming off the bench for the final few moments in the former.
Man United have already let Phil Jones and Axel Tuanzebe move on this summer, while Eric Bailly does not appear to have a future at the club and could also be allowed to depart.
The Red Devils were reportedly pushing to bring Napoli's Kim Min-jae to the club this summer to beef up their backline, but the South Korean is now on the verge of moving to Bayern Munich.