The 24-year-old arrived at Leizpig from Montpellier HSC on a five-year contract in the summer of 2018, and those terms are due to expire in under 18 months' time.
Mukiele has been a consistent part of the team over the past couple of seasons, but at this stage there is nothing to suggest that his contract at Leipzig will be renewed.
As a result, Die Roten Bullen could attempt to recoup a fee for the versatile defender this summer in order to avoid losing him for nothing at the end of next season.
Ralf Rangnick is familiar with Mukiele from his time in the Leipzig offices, and the German is said to be determined to engineer a move for the France international.
However, Foot Mercato reports that Paris Saint-Germain are also in the hunt for Mukiele's services, with sporting director Leonardo identifying the right-back as the perfect fit.
There were rumours of current right-back Achraf Hakimi wanting to leave PSG this summer, but such speculation was recently shot down by the defender's agent.
"He's happy there, we have 4 years left on our contract with PSG. Achraf's young and wants to continue growing at Paris Saint-Germain," agent Alexandro Camano told Como te va.
Nevertheless, Mukiele's versatility makes him an ideal acquisition, with the Frenchman capable of operating as an out-and-out right-back, further up the field, in central defence or in the left-back position.
Mukiele played the full 90 minutes on the right-hand side of Domenico Tedesco's 3-4-2-1 against Augsburg at the weekend, and the former Montpellier man ended the match with three assists to his name.
Mukiele has now taken his tally for the 2021-22 season to two goals and five assists from 37 appearances in all competitions, including 21 starts in the Bundesliga.
The defender has not won a major honour with Leipzig but has now racked up 145 games for the club in the past four years, banking 10 goals and setting up 11 more.
Atletico Madrid and Bayern Munich have also been credited with an interest in the one-cap France international, with the former still aiming to fill the void left by Kieran Trippier's move to Newcastle United.
Interim Man United boss Rangnick has often rotated Aaron Wan-Bissaka and Diogo Dalot in the right-back role this term, with neither man nailing down a starting place for long periods.
The former Leipzig boss expects "six or eight" new signings to be made under new manager Erik ten Hag as the Red Devils prepare for a season without Champions League football.