The Frenchman has been in discussions with Barca over a new deal for some time, but so far no agreement has been struck.
With his current contract set to expire in the summer, the 32-year-old has revealed that he has other options should a conclusion not be reached at the Nou Camp.
"There are clubs that have shown an interest, notably PSG, Milan and Manchester City," Abidal told RMC.
"But there have been no concrete offers and I can't say any more.
"I have a lot of respect for Barca but if we can't reach an agreement, the door is always open."
Abidal joined Barca in 2007 from French club Lyon.