The Belgium attacker has been instrumental for both club and country over the last few years, registering 87 goals and 73 assists for the Blues in 288 games, as well as 21 goals and 22 assists from 82 Red Devils caps.
Hazard is regularly linked with the likes of Real Madrid due to his burgeoning reputation as a world-class talent, but former Blaugrana and Spain captain Puyol believes that the 27-year-old, though "fantastic", still "has plenty of time to grow".
Puyol, speaking to Sky Sports News ahead of Chelsea's Champions League last-16 second leg against Barca, said: "I don't think he's at their level yet. We are talking about incredible players. It's not just one season, they have been at the maximum level for 10 years now.
"For me, Messi is the best player in the world and in history. It's impressive what he's doing every year at an exceptionally high level, breaking records, getting better and better in more aspects of his game.
"So to compare him with Messi or Ronaldo is difficult, but Eden Hazard is a fantastic player. He's a player who makes the difference and has plenty of time to grow."
Puyol made more than 400 appearances across Barca's senior and development teams, and starred 100 times for La Roja.