The Daily Mail claim Hughes, a former Bayern player, has been targeted by the club's president, Uli Hoeness, and an approach may be made in the next few days.
The German giants are also considering Bayern Leverkusen coach Jupp Heynckes and former Stuttgart boss Matthias Sammer, who is currently working for the German Football Federation, according to the Daily Telegraph.
Van Gaal's Bayern have struggled this season and despite winning the Double last term the Dutchman has agreed to leave the club at the end of the Bundesliga campaign.
Hughes, who scored six goals in 18 league games during a loan spell in Munich during the 1987-88 season, signed a one-year deal with Fulham when he replaced Roy Hodgson last summer and would be free to join Bayern without the need for compensation.
The former Manchester United striker began his managerial career with Wales and moved into club football with Blackburn Rovers in 2004, guiding the Lancashire club to three semi-finals before joining Manchester City in 2008.
After billionaire owners Abu Dhabi United Group bought City in 2008, Hughes lasted 18 months before being replaced by Roberto Mancini.