The 35-year-old has been dogged by injury problems over the last couple of seasons and returned to action following two knee operations in October.
However, he has only featured four times in the last three months and has been usurped by 22-year-old Marc Bartra in coach Gerardo Martino's pecking order.
According to the report, Puyol has communicated his intention to retire at the end of the season to fellow players and staff at the club should he not feel an improvement in his fitness in the coming months.
However, the paper also claim that the Spanish international hasn't ruled out the possibility of a move to Qatar or the United States to end his playing days.
Puyol is one of Barcelona's most decorated players of all-time with three Champions League and six La Liga titles to his name.
He is also one of just eight men to have represented Spain 100 times and was a key part of the side that won the European Championships in 2008 and the World Cup in 2010.