The discussions surrounding Messi and Manchester United striker Ronaldo have gone on for years, with neither camp willing to cede an inch in the row of who is the better player.
Messi has made 983 professional appearances, registering 773 goals and 338 assists, while Ronaldo has played 1129 times, scoring 815 goals and grabbing 230 assists.
However, Muller has suggested that his own results against teams including Ronaldo have swayed him in favour of the Portuguese international.
The 33-year-old, who was speaking ahead of Bayern's Champions League match against Barcelona at the Allianz Arena, admitted that his statistics against Ronaldo were 'not that good'.
“I go for Ronaldo,” Muller told ESPN. “Against Messi I have a good statistic, against Ronaldo, not that good.”
In eight appearances against Bayern Munich in the Champions League, Ronaldo has scored nine goals – all of which came in a Real Madrid shirt. The Portugal forward will not come up against Muller in Europe's elite competition this season, unless the 37-year-old secures a move away from Old Trafford in January.
Ronaldo, who expressed his desire to leave United in the summer in search of Champions League football, has made seven appearances for Erik ten Hag's side so far this season, but has failed to record a goal or an assist.