Neymar, 27, could be set to leave the Parc des Princes this close season after sporting director Leonardo confirmed the star was for sale at the right price.
The Brazil international left Barca in a world-record €222 million move two years ago, but he has been strongly linked with a return to Camp Nou.
Former Barcelona captain Puyol, who won 18 trophies with the club, said the past should have no impact on the La Liga champions' decision.
"In the end, you have to value the present, not so much the past," Puyol said on Monday, via Spanish media.
"If the player is on the market and you need him, you don't have to be thinking about what happened a few years ago."
Neymar has still starred in two seasons with PSG, but both campaigns have been hampered by injuries.
The Brazil star also recently missed out on the Copa America following an injury against Qatar in a pre-tournament friendly, although Brazil went on to win the tournament on home soil by topping Peru in the tournament finale.
However, Puyol believes the star forward can still deliver plenty for Barcelona.
"Neymar is a great player who can make a difference," he said.
"He's not been able to play his best football [at PSG] because of injuries, but he still has a lot to give to football."
Camp Nou legend Lobo Carrasco isn't on the same page as Puyol when it comes to the Brazilian however, declaring the club must get its priorities right.
“I do not want Neymar to come in," Carrasco told El Chiringuito.
“Barca needs to have a Puyol. With the signing of Neymar, Barca would lose even more at the back."
While a return to Barcelona remains uncertain, Neymar's future at PSG appears in serious doubt after he failed to report on time for pre-season.
The Ligue 1 champions declaring appropriate measures will be taken as a result - though Neymar's father is adamant the club were aware of his son's plans.