Barcelona's Eric Abidal holds up a flag (Photo: Reuters)
"Eric Abidal has received a very interesting offer to join Paris Saint-Germain," the Barcelona-based daily Sport said.
"The French club would give him a three-year contract, which could lead the French player to question his future at Barcelona."
Barcelona have offered Abidal a one-year renewal of his contract with a further year negotiable, but the player wants a fixed two-year deal, Sport said.
The 32-year-old left-back was in the form of his life last season before a tumour was discovered on his liver in March.
However, after undergoing surgery he made a rapid recovery, and after returning to action on May 3 he also appeared in Barca's Champions League final win over Manchester United at Wembley.
PSG have embarked upon an ambitious recruitment programme since being taken over by Qatar Sports Investments (QSI) in May.
The club signed Abidal's France team-mates Kevin Gameiro, Blaise Matuidi and Jeremy Menez over the summer and also broke the French transfer record by signing Javier Pastore from Palermo for 42 million euros ($59.4m).