The Red Devils completed the signings of Matthias de Ligt and Noussair Mazraoui from the Bavarian giants in the summer and they could repeat the trick this winter with two more out-of-favour stars.
Erik ten Hag's side have made a poor start to the season despite their large transfer spend in recent windows and are reportedly keen to further bolster their ranks in January.
Goretzka has been handed just a minute of action in the Bundesliga this season under Vincent Kompany, while Sane has fared only marginally better with 32 minutes from Bayern's first six fixtures.
Manchester United are reportedly interested in signing (L-R) Leon Goretzka, Alphonso Davies and Leroy Sane
According to the report, the Red Devils are interested in acquiring a central defensive midfielder, despite the costly outlay on Manuel Ugarte from PSG two months ago.
However, Goretzka is reportedly keen on remaining with the Bundesliga giants beyond the January transfer window, while Sane is in discussions with the club over a new contract.
Another name rumoured to be on the Premier League side's radar is Alphonso Davies, whose deal at Bayern expires at the end of the season. The 23-year-old has been heavily linked with a move to Real Madrid in recent seasons.
Davies' arrival would address the biggest weakness in the United squad, with Ten Hag currently without a recognised left-back following the ongoing injury problems of Luke Shaw and Tyrell Malacia.
Unlike his team-mates, Davies has been a regular starter for Kompany this season and has featured in all but one of the side's league fixtures in their unbeaten start to the campaign.
United return to Premier League action against Brentford this weekend, hoping to rapidly improve their lowly position after a dismal start.
Ten Hag appears to have staved off the latest immediate threat of the sack but the Dutchman will be acutely aware of how quickly things can change.
His side travel to Istanbul to take on Jose Mourinho's Fenerbahce side after their clash against the Bees on Saturday before facing West Ham and Chelsea in their subsequent league outings.