The versatile France international - who is comfortable as a centre-back and full-back - has entered the final year of his contract with the German champions and is not expected to sign an extension.
Pavard remains a key part of Thomas Tuchel's plans, but he is thought to be keen to take on a new challenge away from Bavaria, and Bayern are prepared to let him leave for the right price.
Man United are rumoured to have seen one bid for the 27-year-old turned down by their German counterparts, who are demanding a €30m (£25.9m) figure to sanction a summer sale.
The Red Devils are believed to be some way off Bayern's valuation at present, but talks are ongoing as all parties seek to find an agreement before the window slams shut.
According to Sky Sports News, Pavard himself is ready to push for a potential transfer to Old Trafford, and he will "fight as hard as possible" to engineer his dream move.
The Red Devils have already waved goodbye to Phil Jones and Axel Tuanzebe on free transfers, while Al-Nassr-linked Eric Bailly is also expected to leave the club imminently.
However, Pavard will only be able to join Erik ten Hag's team if Harry Maguire is cut from the ranks, as West Ham United try to finalise a £30m deal to sign the England centre-back.
Hammers boss David Moyes has confirmed that his side have had a bid accepted, but they are yet to find common ground over personal terms with Maguire, who may supposedly have to take a £70,000-a-week pay cut at the London Stadium.
As a result, West Ham could allegedly turn their attention to Bayer Leverkusen's Odilon Kossounou instead, which would threaten to scupper Pavard's proposed arrival at the Theatre of Dreams, but he will do everything in his power to ensure that a deal is struck.
The former Lille and Stuttgart man was also believed to be on Chelsea and Barcelona's radar, although the latter team are now pursuing a deal for Manchester City outcast Joao Cancelo instead.
In spite of the fact that Pavard could leave for nothing in 2024, the report adds that Bayern could be prepared to demand as much as £35m, having missed out on a deal for Manchester City's Kyle Walker.
Pavard - who won the 2018 World Cup with France - has come up with 12 goals and 12 assists in 163 matches for Bayern, including seven strikes in all tournaments during the 2022-23 campaign.
The 27-year-old started Saturday's DFL Super Cup showdown with RB Leipzig at right-back, but he was withdrawn at the break as Tuchel's side were embarrassed in a 3-0 loss.
Should a deal for Pavard fall through, Man United are believed to be considering Nice's Jean-Clair Todibo as an alternative addition to their defensive ranks.