The French full-back has been locked in talks with the reigning European champions for some time but is yet to put pen to paper.
It is expected that fresh terms will be thrashed out, but for now his future remains uncertain.
Barca's failure to tie him down has led a number of other clubs to put out tentative feelers regarding his availability.
Premier League leaders City are among those to have expressed an interest, with Abidal confirming that initial contact has been made.
"There are clubs that have shown an interest, notably PSG, Milan and Manchester City," the 32-year-old 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 has also claimed that he is planning to play on for at least two more years.
He added: "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."