Mukiele only has one year left to run on his existing contract at the Red Bull Arena and could therefore be allowed to leave for a cut-price fee this summer.
Manchester United were said to have been interested in a deal for the 24-year-old, who worked under former Red Devils interim manager Ralf Rangnick in Germany.
However, Man United have seemingly dropped their interest in Mukiele, with Diogo Dalot set to be Erik ten Hag's first-choice right-back for the start of the new season.
As a result, L'Equipe - via Get French Football News - claims that PSG are now in 'advanced talks' over a deal to sign the France international before he leaves Leipzig on a free transfer in 2023.
The report adds that Mukiele has already reached an agreement in principle over personal terms with the Ligue 1 champions, and football advisor Luis Campos had earmarked the versatile Frenchman as a priority target after arriving in Paris.
PSG can supposedly expect to pay in excess of €10m (£8.5m) to sign Mukiele, who previously spent nine years on the books at Paris FC as a youth player between 2004 and 2013.
Mukiele then rose through the youth ranks at Lorient before joining Montpellier HSC in 2017, but he only spent one-and-a-half years at the Stade de la Mosson before heading to Leipzig.
The one-cap France international has since scored 10 goals and provided 11 assists in 145 games for Die Roten Bullen, including two goals and five assists from 38 outings last term.
Mukiele won his first piece of silverware with Leipzig last term in the form of the DFB-Pokal, playing 59 minutes of the final win over Freiburg as a substitute.
Mukiele has primarily featured in a three-man defence or as a right-wing back for Leipzig, and new PSG manager Christophe Galtier is experimenting with a back three in pre-season.
The versatile 24-year-old could therefore arrive at PSG to compete for the right-wing back spot with Achraf Hakimi after Colin Dagba joined Strasbourg on loan.
Alternatively, Mukiele may provide backup to Marquinhos, Sergio Ramos and Presnel Kimpembe at centre-back, although the latter continues to be linked with a move to Chelsea.
PSG have already signed Vitinha and Hugo Ekitike this summer, with the latter joining on loan from Reims, and Nuno Mendes has made his move from Sporting Lisbon permanent.
Galtier's side continued their pre-season preparations in ideal fashion on Wednesday, beating Japanese champions Kawasaki Frontale 2-1 thanks to goals from Lionel Messi and Arnaud Kalimuendo.