Joachim Loew thinks equally highly of Mueller, who was given the lone striker role by Guardiola in preference to the more likely candidates Claudio Pizarro and Mario Mandzukic for last weekend's game at Bayer Leverkusen - hardly the sort of encounter in which to merely experiment.
"I've watched him recently, and he's done that really well for Bayern," said Loew, who has to choose between Mueller and in-form Max Kruse for the spearhead of his 4-2-3-1 in Cologne for Friday's World Cup qualifier against Ireland.
It was perhaps a portent the pair arrived at the squad's Duesseldorf hotel together, with Loew suggesting they are neck-and-neck in his pecking order: "Both could play as attacker against Ireland. In the end, it doesn't matter who plays. I'm not worried. On the contrary, I don't see us having a striker problem."
He is perhaps right. Given Marco Reus, Lukas Podolski - both injured for the Ireland game - Mario Goetze, Andre Schuerrle, Sidney Sam and Toni Kroos can all score goals as attacking midfielders, perhaps the lack of a natural successor to Klose, now 35, and competition for Gomez is not even necessary. Goetze even played as a false nine with a degree of success against Kazakhstan last season.
But despite the almost indecent wealth of talent slightly further back down the pitch, the fact most Bundesliga teams play a classic 4-2-3-1, and the fact most Nationalmannschaft players are domestic-based, it would make more sense for Loew to adopt a formation in which they feel comfortable.
To do that, he needs more options in terms of strikers, and if Stefan Kiessling is to remain ignored, Mueller, who has mostly had a wide attacking midfield role at Bayern since breaking into the first team under Juergen Klinsmann, fits the bill most snugly.
Top scorer at the 2010 World Cup, Mueller has a goalscorer's instinct that Kruse does not. "I don't see myself as a classic central striker," said the Borussia Moenchengladbach man recently, whereas none other than Oliver Bierhoff, Euro 96 hero-turned-team-manager, said of Mueller: "Thomas is a constant thorn in the side, he's unpredictable and is always looking to finish things."
Though certainly far from orthodox in the role - "He's always doing crazy things up there, that's why he's always dangerous," said Bastian Schweinsteiger recently - Mueller has a proven track record in front of goal. Though Kruse's figures of 38 goals and 39 assists in 139 league games stand up to Mueller's of 46 strikes and 53 assists in 142 Bundesliga encounters, Kruse has had two seasons at 2. Bundesliga level to sandbag his stats while Mueller's have all been in the top flight.
His tireless work ethic and clear hatred of mediocrity - he has been seen to stomp through the Allianz Arena mixed zone on many an occasion with a scowl longer than a Bayern unbeaten run - make Mueller ideal as the man to press first when Germany do not have the ball, even more so than the less mobile Gomez and (also much older) Klose.
Kruse, for all his excellent start to the season, seems to need more support around him; Mueller has the determination, the track record and the talent to make himself Germany's number one striker for the next six-eight years.
Ian Holyman | @ian_holyman
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