United were linked with a number of central defenders ahead of the 2018-19 campaign, with Boateng emerging as a reported target in the latter stages of the window.
Boateng has now revealed that there was interest from United in his services, but the 30-year-old, who also had an offer from Paris Saint-Germain, was not prepared to leave the Allianz Arena.
"I had enquiries from PSG and Manchester United," Boateng told Bild. "I did not want just to get away from Bayern, but I was thrilled to try a new challenge. I feel well at Bayern. It's one of the biggest clubs in the world.
"I called Jose Mourinho, I told him that his interest was an honour for me and thanked him for trying so hard for me. I explained to Jose that it's difficult to leave Bayern, and if I do, everything has to be in place to top this club."
Boateng has made over 260 appearances for Bayern since a move from Manchester City in 2011. The Germany international has also won six Bundesliga titles and the Champions League during his time in Munich.