The 35-year-old believes the PSG defender would be a great signing for the club, as he says injuries last year have showed a need to strengthen in that position.
The Brazil defender, 28, who moved to the French capital last season from AC Milan, has been heavily linked with the Blaugrana despite having four years remaining on his contract.
The Catalan giants suffered from a dearth of quality in the heart of their defense last season following injuries and suspensions to key players, but Puyol believes some of these issues can be amended with the Brazilian in the team.
“The center of defense is a position hit hard by injuries,” Puyol told reporters. “Thiago is one of the best center backs in the world, and I think he would adapt well to Barcelona.”
Puyol was also saddened by the departure of Tito Vilanova, who suffered a cancer relapse, but he knows the club must move on and provided his opinion on potential replacements, which included Celta Vigo coach Luis Enrique and Newell’s Old Boys boss Gerardo "Tata" Martino.
“We have a very specific way of playing, and the coaches linked to this job will come in and follow that style. We all want the best for the club, so I trust whoever they bring in will be fine," Puyol said. “I have a good relationship with Luis Enrique and I have trained with him before. He is one of the most accomplished names out there, but I like all the others as well.
"I know Tata is a good coach and I really like his style of play. He is very complex and tough on his players. He does not let them train easily."