The 25-year-old was linked with a switch to the Red Devils during his time at RB Leipzig, but he ultimately made the move to Paris Saint-Germain in July 2022.
Mukiele featured on 25 occasions for PSG during the 2022-23 campaign, but he has been restricted to just seven minutes of action for the French champions this season.
There is already speculation surrounding the Frenchman's long-term future in Paris, and according to FootballTransfers, Man United could move for him during the January window.
The report claims that Mukiele is seen as a 'viable target', with PSG believed to be open to letting him depart for the right price during the winter market.
Diogo Dalot and Aaron Wan-Bissaka are the two senior right-backs at Old Trafford, but the latter is currently on the sidelines with a muscular problem, while the former has found it difficult to impress this term.
Man United were expected to move for a right-back over the summer, with Bayer Leverkusen's Jeremie Frimpong heavily linked with a switch to Old Trafford.
However, Wan-Bissaka stayed despite being linked with an exit earlier this year, with the Englishman impressing in the second half of last season.
Wan-Bissaka started the campaign as the first-choice right-back, but Dalot is currently being used in that area due to an injury for the former Crystal Palace youngster.
Ten Hag is thought to have concerns over Wan-Bissaka's 'personality', believing that he does not have the mindset required to be a part of a successful team.
Meanwhile, Dalot's 'defensive stability' is said to concern the Man United head coach, who is under pressure following six defeats in 10 games in all competitions this season.
The 20-time English champions currently have big defensive problems, as three left-backs are also injured in the shape of Luke Shaw, Tyrell Malacia and Sergio Reguilon.
Lisandro Martinez has undergone a foot operation, meanwhile, with the centre-back set to be on the sidelines for the next two to three months while he recovers.
Man United are also believed to be keen to sign a new attacker in January, with Jadon Sancho widely expected to leave following his falling-out with Ten Hag.