Not long after the 2010 World Cup, when asked in an interview how he would best explain his position and role on the pitch, Mueller's reply was simple and concise.
Roughly translating as "space investigator," it attempts to capture the sometimes intangible qualities Mueller brings to Bayern Munich and the German national team.
Not blessed with blistering pace or explosive power, two traits often deemed essential in the modern game, Mueller's advantage comes from intelligence and movement, exploiting spaces most players don't even see.
"I'm a player that makes many runs off the ball, hurting the opponent's defense," Mueller tells Copa90.
"Football is always a mix between pass play and run play, you've got to make intelligent runs without getting impatient and, of course, always work on the finish during practice."
When Mueller was 10 years old, Bayern Munich held a tournament called the Mercure Cup in the vicinity of the city, searching for talented kids in the area.
A scout from the club was there to watch and Mueller, by his own admission, played "pretty well" for his team.
Already an avid Bayern fan as a kid, Mueller was adamant this opportunity wasn't going to pass him by.
"Mum, we really need to go," he recalls telling her. "I have a trial!"
Later that same year, in July 2000, Mueller received his first official playing membership at Bayern and admits his first training session came as a bit of a shock.
"I thought I was pretty decent," he says. "But I came to Bayern and realized that: 'Oh, there are other great players on this planet.'"
Mueller believes the academy experience forms the basis of any footballer's professional career. He says sacrifices will always need to be made, but players shouldn't forget why they first started playing the sport.
"Here (the academy), everybody is together and the conditions are great, all players, all trainers, working together on a daily basis, to improve every player," he says.
"You have to give up a few things and even suffer a bit, but you must never lose the fun of it."
Managers, both at Bayern and the German national team, have been and gone in Mueller's time, but he has always remained a key figure on the pitch.
The 28-year-old, who is modest and endearingly down to earth, attributes this to his attitude, something which has never changed since his days in Bayern's youth system.
"I had many trainers and got along with all of them as I was someone who always wanted to win and was willing to put in the effort," he says. "That's why we never had any issues.
"There is no single word that sums up everything, but a combination of ambition and discipline with the joy for football and life in general.
"You've got to find a good balance between team spirit and egoism. The rest just happens."
Bayern Munich academy
Mueller describes the privilege of playing in Bayern's youth system as "definitively something special."
He returns to that word again -- "special" -- when recalling his debut for the club's reserve team, which currently plies its trade in the German fourth tier.
"Although we lost, when I came on I scored straight away and it feels good to impress the new coach a bit," he says .
"Every year you have the pressure to make it into the next better team and, naturally, at some point when I was 16 or 17, I played for the Youth National Team ... and you think: 'How far can I get?'
"But that is all in the stars, in the future."
Though hard work and commitment are undoubtedly the cornerstones of any successful professional career, Mueller realizes that luck also plays a part.
"You've got to be able to achieve top performance at the right time, on the right day," he says.
Mueller was given his Bundesliga debut a month shy of his 19th birthday by German coach Jurgen Klinsmann, but says he barely has any memory of that day as he "only played 10 minutes."
The early memory he cherishes more than any other is his first goal for Bayern, which came in the 7-1 demolition of Sporting Lisbon in the Champions League.
Demonstrating the "Raumdeuter"' qualities that would later go on to define him, Mueller somehow found space, just two yards from goal, in a crowded box of 15 players.
He tapped the ball into the empty net, just 20 minutes after coming on, to complete the rout of the Portuguese side.
"It was obviously pure euphoria," he says. "You don't forget that any time soon."
Bayern Munich go into Wednesday's second leg of their Champions League round of 16 clash against Besiktas with an insurmountable 5-0 advantage.
Mueller, who scored one goal and assisted another in the first leg demolition in Munich, is chasing his second European Cup.
But with multiple Bundesliga titles and Champions League and World Cup winners' medals around his neck, his status as a legend of German football is already confirmed.
Mueller now looks to impart some of his wisdom on the next generation of Bayern players.
"With this business, when you look at the academy, the pressure on the young players in pretty big," he says. "
"You want to be a role model to them because everybody who lives here at the academy, plays and trains here, is someone special and has a big chance to make it to the top.
"For FC Bayern, it's very important that in the future that players from their own youth academy are able to climb the ladder."