The former Spain defender came up against the Uruguay star during his playing days and believes he would be a fine addition to the Camp Nou ranks
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Suarez has just started a four-month ban for biting Italy defender Giorgio Chiellini during the World Cup but that has not deterred Barca, nor has Liverpool's determination to hold out for a £80 million fee.
Numerous Barca figures have openly spoken of their admiration for Suarez with Puyol, who will work under sporting director Andoni Zubizarreta next season after opting to end his playing career, the latest.
He told El Mundo Deportivo: "Luis Suarez is a great striker. I've played against him. All of the names that have been mentioned with Barcelona are good and we will have to wait and see who comes in the end."
He added, however: "As a player you have a responsibility. A lot of people look at us and we have to be aware of that and control our actions because children want to imitate us."
Suarez scored 31 goals in 33 Premier League games last season and would be a welcome addition to a Barcelona squad which, on the face of it, is also in need of strengthening in defence.
Although his latter years were plagued by injuries, Puyol's retirement has still left them short of a commanding central defender.
Yet the 36-year-old does not believe the situation is as bleak as others have portrayed, adding: "The club already has some good central defenders. It's not easy to find players who have the qualities to play for Barcelona.
"We need to leave Zubizarreta and his team to find the right players, but they already have Javier Mascherano, Gerard Pique and Marc Bartra. It's very difficult to improve on their level."
Meanwhile, Barca will be delighted to know that Suarez is available to undergo a medical should he choose to leave Liverpool, despite being banned from all football activity for four months, according to Fifa disciplinary chief Claudio Sulser.
He said: "The player cannot have any activity related to football, but a medical examination for a transfer yes – the sanction is not linked to transfer rights."