Kurzawa has been in high demand, with his contract at the Parc des Princes set to expire on June 30.
Among his potential suitors are Arsenal, who were rumoured to be after him back in January.
Sport, however, reports Barcelona have now moved ahead of the Gunners in the race to sign the 27-year-old.
Kurzawa is being chased by TEN clubs as his five years in Paris dwindle to a close.
But Barcelona are the player's number one choice.