Muller grabbed 85 goals for Bayern Munich and West Germany in 1972 and the mark stood for 40 years until Messi netted his 85th and 86th goals of an incredible 2012 in Barca's 2-1 win at Real Betis.
"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," The Telegraph quoted Muller, as saying.
According to the paper, 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 said.
"He's fantastic. He only has one defect and that is that he doesn't play for Bayern Munich," he added.
Messi's Barca team-mates were also in awe of his achievement, the paper said.
"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," Spain defender Gerard Pique said. (ANI )