The France international will see his current deal at Camp Nou expire at the end of the season.
Barca have been locked in extension talks for some time, with it their desire to keep the 32-year-old in Catalunya.
Abidal is yet to agree fresh terms, though, and has hinted in the past that he may end his five-year association with the Primera Liga giants.
A return to France has been touted, while a move to the Premier League has also been mooted.
Arsenal could offer him a route to England, with the Gunners currently short on defensive options.
Arsene Wenger has no fit full-backs at present, so he could be tempted to make a move during the winter transfer window.
Abidal would add considerable experience to the Emirates Stadium ranks, with domestic and European success having been enjoyed during his time at Lyon and Barcelona.
He has also been capped 60 times by his country, featuring at two World Cup finals and Euro 2008.