The Argentine requested to leave Barcelona in the summer but decided to stay and honour the final year of his contract at the Catalan side - and Puyol now feels that Messi could be at Barca for years to come.
The club's former captain said: "Like any fan, I did not want Messi to leave, but this is football.
"In the end he decided to stay. He recently said that he is motivated, that he wants to win and we hope he can continue with us for many years.
"He is a huge asset for La Liga, he is one of the best in the world."
Puyol spent his entire career at Barcelona and admits he could understand if Messi ever decided to leave, as he had previously hoped to play alongside his idol Paolo Maldini at AC Milan.
He explained: "In 2014, after my injury, I chose to retire despite the offers from English and Italian clubs. When your club is also your home you don't feel like wearing another shirt.
"I would have loved to go to Milan to play with Maldini, my idol. The Rossoneri will be back, even if they are going through a difficult moment now. I would have been happy to end my career in Italy."