Mueller grabbed 85 goals for Bayern Munich and West Germany in 1972 and the mark stood for 40 years until Sunday night when Messi netted his 85th and 86th goals of an incredible 2012 in Barca's 2-1 win at Real Betis.
Mueller led the tributes, telling Sport1.de: "My record stood for 40 years - 85 goals in 60 games - and now the best player in the world has broken it, and I'm delighted for him. He is an incredible player, gigantic."
Mueller, whose record as Germany's all-time top goalscorer is also under threat from Miroslav Klose, now hopes Messi will add to his tally before the end of the year.
"He's such a nice and modest professional and I hope he gets one or two more goals in 2012 and that he can then hold onto the record for the next 40 years," he added. "He's fantastic. He only has one defect and that is that he doesn't play for Bayern Munich!"
Messi's Barca team-mates were also in awe of his achievement. Spain defender Gerard Pique told El Mundo Deportivo: "Leo is supernatural, he has no limits and we always have to remember everything that he's given us. We have to enjoy him every single minute that we have him now."
As well as passing Mueller, Messi's double against Betis sent him clear of Cesar Rodriguez as Barca's all-time leading league goalscorer after they had been level on 192 before the match. Earlier this year Messi became Barca's record scorer after moving past the tally of 232 official goals set by Rodriguez during the 1940s and 50s.
Barca sporting director Andoni Zubizarreta believes the magnitude of Messi's achievements may not fully sink in until further down the line. "I'm sure that we will really appreciate Leo's records over time. They happen so quickly that they seem to be just one more thing. It all seems very simple but it's very difficult to describe it," he told Canal Plus.
The man himself was typically modest and insisted he derived more pleasure from helping Barca preserve their six-point advantage at the top of the Primera Division standings than he did claiming another personal landmark.
"The record is great for what it means, but the most important thing is that the team won and that we maintained the distance with the teams behind us," Messi told the club's website. But he added: "I'll try to score more goals to make it more difficult for the next player that tries to break it."
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