The centre-back, 24, only joined Bayern from Juventus in July last year, but he is said to be unhappy with his lack of playing time for the Bundesliga champions.
De Ligt – who has won 43 caps for the Netherlands – previously played under United boss Erik ten Hag at Ajax, who sold him to Juve for €75m (£67.8m) in the summer of 2019.
According to Fichajes, Man United are monitoring De Ligt with a view to a potential move – which could contain a surprise swap element.
Scott McTominay was linked with a shock switch to Bayern during the last transfer window, before the Bavarian giants came close to signing Joao Palhinha from Fulham – only for that deal to fall through.
Why Man United's problems are EVEN WORSE than you think
Could McTominay be used as a makeweight in a bid for De Ligt? Perhaps – and United might well need that kind of helping hand.
Transfermarkt currently values De Ligt at €75m (£65), with Bayern thought to price him at €80m (£69m).
Man United were rumoured to be chasing De Ligt's former Bayern teammate Benjamin Pavard over the summer – but the France defender ultimately joined Inter Milan.
There was just one new defensive arrival at Old Trafford ahead of the 2023/24 campaign: Jonny Evans, who penned a one-year contract after initially returning to United on a short-term basis to play in pre-season.
More Manchester United transfer stories
The window may be closed for now, but Manchester United transfer news keeps coming thick and fast.
The Red Devils are also being linked with a stunning January swoop for an ex-Arsenal forward.
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