United boss Jose Mourinho is keen to sign a new centre-back before the end of the transfer window, and the likes of Toby Alderweireld, Harry Maguire and Yerry Mina have all been linked with a switch to Old Trafford.
However, according to Bild, the Premier League giants are still interested in Boateng and contact has been made with the Bundesliga champions.
Boateng has previously indicated that he would like to secure a new challenge before the end of the summer, and Bayern are said to be willing to part ways with the Germany international for the right price.
Bayern allegedly value Boateng - who has previously represented Manchester City in the Premier League - in the region of £44.5m.
The two clubs squared off in a friendly on Sunday evening, with Bayern prevailing by a 1-0 scoreline at the Allianz Arena.