The 26-year-old was linked with a number of clubs during his time at RB Leipzig, including Manchester United, but he moved to PSG in the summer of 2022.
Mukiele has struggled for action during the 2023-24 campaign, only making 10 appearances in all competitions, and there has been speculation surrounding his future.
According to transfer expert Fabrizio Romano, discussions between Bayern and PSG are taking place, with the Bundesliga giants keen to sign him before the end of the month.
Romano claims that Bayern head coach Thomas Tuchel has 'approved the move', while Mukiele is also pushing to secure a switch to Allianz Arena before the winter window closes for business.
Meanwhile, according to The Mirror, West Ham United are preparing to step up their interest in Sunderland's Jack Clarke, with the attacker identified as a leading January target for the Hammers.
Clarke joined Tottenham Hotspur from Leeds United in 2019, but he struggled to make his mark for the North London club, representing them just four times, before joining Sunderland permanently in 2022 after a loan spell in the second half of the 2021-22 season.
The 23-year-old has scored 25 goals and registered 20 assists in 99 appearances for the Black Cats, including 13 goals and two assists in 29 outings in all competitions this term.
Burnley were heavily linked with Clarke over the summer, but the strongest interest is now said to be coming from West Ham, who are under pressure to sign a home-grown player this month.
Sunderland will demand a high fee for the Englishman, though, as Tottenham have a 25% sell-on clause.
Staying in the Premier League, Jamaal Lascelles could reportedly be leaving Newcastle United before the end of the transfer window, with Besiktas keen on his services.
The 30-year-old has made 22 appearances for the Magpies this season, but he is down the pecking order when head coach Eddie Howe has a full squad available.
Lascelles was an unused substitute in Newcastle's 3-2 loss to Manchester City in the Premier League on Saturday, and he has less than six months to run on his current deal.
According to The Sun, Besiktas have identified him as a leading target, with the Turkish giants planning to make an offer in the near future.
The report claims that the Istanbul outfit are looking for a replacement for Eric Bailly, and Lascelles is viewed as a realistic addition before the January market closes.
Lascelles has made 246 appearances for Newcastle since arriving from Nottingham Forest in 2014.