Fabregas has long been linked with a return to Barca, the club where he learnt his trade as a youngster before moving to Arsenal seven years ago as a 16-year-old.
During his time in England Fabregas has developed into one of Europe's best midfielders and Barca, having last week spent 40 million euros on snapping up prolific Valencia striker David Villa, now look to have their sights set on bringing the 23-year-old back to the club.
Puyol, speaking at a press conference with Spain on Tuesday, believes Fabregas would be a great addition to the Spanish champions' squad.
"Cesc is an excellent player and a great friend. For me, he would be perfect for Barcelona. I would love to see him with the azulgrana, but we need to respect that he has a contract with his club," said Puyol.
Fabregas, who has a contract with Arsenal until 2014, revealed recently at a promotional event in Spain that he would like to return to Barca, and his father Francesc Fabregas confirmed today that the playmaker wants the transfer completed "as soon as possible".
Puyol said of his Spain squad-mate: "It's very unusual to see Cesc nervous, but all this is a little problematic for him, because it's a matter that is being talked about daily and he has fans, a coach and team-mates that he needs to respect."
However, it seems that there may be no quick resolution to what could be a long-running transfer saga.
Barca corporate director general Joan Oliver confirmed on Monday evening they have been in contact with Arsenal regarding Fabregas but insists they have not yet made an offer.
Oliver also said there was no deadline by which time Barca hoped to seal the signing of the Arsenal talisman.
"Still there is no offer. It's true that the player has shown his desire to play at Barca, possibly this season. We have made a first contact with Arsenal, letting them know our intention to talk and this is the current state of the situation," Oliver said on his club's website.
"There is no time-frame. The period is from today and until the deadline for registering players at the end of August.
"We are in no rush and you never know how long these operations can last."
Francesc Fabregas, who is also Cesc's agent, also believes that talks between the clubs could be protracted. However, he feels in the end that Arsenal could give the green light for their captain to leave.
"The negotiations between Arsenal and Barcelona are going to be very long," Francesc Fabregas was quoted as saying on Radio Marca.
"Both parties are going to have to sit down several times because the matter is complicated.
"Cesc is now focused on the Spanish national team, but he wants the signing to be closed as soon as possible.
"I don't know how this is going to end up, but I think that we need to respect the decision and the will of the player.
"Cesc has always responded to Arsene Wenger with his work and we are also grateful to Arsenal because they have made our son a man. We only want this to end soon.
"At the moment he has a contract with Arsenal. I get the feeling the English club don't want to sell him but in the end will allow Cesc to leave."