The former Blaugrana midfielder has been in talks to re-join the club following Ronald Koeman's sacking last week.
Xavi is currently managing Al Sadd in Qatar and is keen to overhaul Barcelona's backroom staff should he join.
Miquel Blazquez has claimed one man involved with that is Puyol, who was captain for most of Xavi's playing career at the Camp Nou.
:rotating_light:A Xavi Hernández le encantaría contar con Carles Puyol para su nuevo proyecto en Can Barça. El entrenador de Terrassa considera que es importante recuperar el carácter y la identidad acompañado de figuras históricas del club azulgrana. #FCBarcelona pic.twitter.com/uj9VnaDOHp
- Miquel Blázquez (@BlazquezFont) October 31, 2021
It's believed Xavi wants Barcelona legends to be more involved in his regime and thinks Puyol is a perfect candidate.
Puyol was a no-nonsense defender and his 'warrior mentality' is still admired across the footballing world.
Barcelona could likely do with that, as they currently sit ninth in La Liga after 11 games.
They drew 1-1 with Deportivo Alaves on Saturday and defender Jordi Alba expressed his frustration at the result.
"It's a bad point, one from nine, a team like Barca needs more. We are not happy with where we are in the table. It's really tough for us to score goals. We put pressure on but we're not scoring," he said.
"They didn't have too many chances but we had some. Memphis [Depay] hit the post but the goal wouldn't go in."
President Joan Laporta revealed over the weekend he is currently in talks with 41-year-old Xavi.
Laporta said per BBC Sport: "I have always said one day [Xavi] will be Barca's head coach but I don't know when.
"We have great references about Xavi at Al Sadd. All our reports about Xavi are positive.
"We can talk a lot about Xavi, but I cannot give you more details. He is in all the papers, but we also have other options."
Al Sadd have said Xavi will be seeing out the two years remaining on his contract.
If Puyol is coming in, any chance we can have Andres Iniesta in the future? Those two reuniting in the dugout...