Sport Bild's Christian Falk reported as much on Twitter:
Per Ryan Taylor of the Express, United have been linked with Muller in the past, with the club said to have failed in an attempt to sign him in 2015.
The 30-year-old has started just three of Bayern's eight Bundesliga matches this season and one of their three UEFA Champions League games.
Falk reported earlier in October that Muller is eyeing an exit from the club in the winter:
The player himself has dropped hints he would look at a move away if his situation does not improve:
Muller has spent his entire career with Bayern, contributing 186 goals and 173 assists in 497 senior matches.
His efforts have contributed to eight Bundesliga titles, five DFB-Pokals and the UEFA Champions League.
He also helped win the 2014 FIFA World Cup for Germany, with whom he has 38 goals in 100 appearances.
The forward was at his peak when the links to United were at their strongest. From the 2012-13 campaign to the 2015-16 season, he scored 102 goals and assisted 61 for Bayern.
Football writer Kaustubh Pandey isn't convinced Muller—who has only reached double figures for goals once since 2015-16—would be the best option for the Red Devils at this point:
Kaustubh Pandey @Kaus_Pandey17
There is nothing wrong in United signing a player like Thomas Muller. Still a quality player. But not the sort United need. He's 30 and the sort of declining 'superstar' players that Woodward will love because it will boost the jersey sales. There are better options out there.
Squawka's Muhammad Butt suggested he could be a shrewd addition:
Muller only turned 30 in September, so he could still have several more years at the top level.
However, his contributions have been diminishing in recent years, hence his situation at the Allianz Arena.
If United could coax him back to his best form, he could be an enormous asset, but he'd be something of a gamble.