Muller led the tributes on Monday, 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."
Muller, 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!"