The France international defender has yet to renew his current deal with the European champions, and has left the door open for a move away from the Catalan giants.
The big spending Premier League club are not the only interested party according to the left-back, who has eyed two more years at the top level.
“There are some clubs interested, like Paris Saint-Germain, AC Milan and Manchester City,” the 32-year-old told RMC Sport.
“At the moment there are no concrete offers. I can’t say any more. I have so much respect for Barca but if I don’t reach an agreement, the door is open.
“I believe I have the legs to go on for two more years. I have an international objective. We have qualified for Euro 2012, which is good, but I am also looking at the 2014 World Cup,” he concluded.
Abidal recovered from a liver tumour last year to feature in the tail-end of Barcelona’s victorious Champions League and La Liga campaigns, but is no longer guaranteed an automatic starting berth in Pep Guardiola’s team.
A move by City would seem unlikely however, as they currently have both Gael Clichy and Aleksandar Kolarov in Abidal’s position.
By Gareth McKnight