Bayern, who were beaten at home in midweek by Bordeaux to severely dent their hopes of qualifying for the knockout stages of the Champions League, could not find a winner in the second half and trail German leaders Bayer Leverkusen by six points.
Berbatov has begun 20 Premier League games, scoring 12 goals, but has been a substitute for each of United's games in the knockout stages of the Champions League.
On Tuesday, McLeish became the first manager of a Scottish club to reach the knockout stage of the Champions League after the 1-1 draw at Ibrox with Inter Milan.