Puyol, the former Barcelona captain, was delighted to see Messi stay at the Camp Nou despite his public stance of wanting to leave.
The six-time Ballon d’Or winner looked set to quit Barcelona at one stage during the summer and he believed there was an exit clause in his contract that would allow him to leave for free.
Manchester City were tipped to sign the Argentina international but once Barcelona made it clear the exit clause had expired, he said he would honour the final year of his contract.
Messi would be free to leave the club in 2021, with Man City still hoping to sign him, but he could easily end up extending his stay in Barcelona.
And Puyol thinks Messi can be convinced to remain at the club.
‘Like any fan, I did not want Messi to leave, but this is football,’ former Blaugrana captain Puyol told reporters.
‘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.
Messi has scored three goals in all competitions so far this season in five matches.