The 33-year-old, who has not been offered a new deal by the Catalan giants, could be officially announced as a Monaco player as early as next week.
There has been plenty of interest in the France international, although it appears that the player's former club Monaco have won the race for his signature.
Abidal's agent, David Ventidelli, has revealed there are other offers to consider, but expects negotiations to be settled soon.
Ventidelli told Fichajes: "[Monaco, Lyon and Montpellier] are interested in Abidal. There's interest from other leagues too, but Eric's preference is to return to France for family reasons. Monaco are his number one choice.
"[The Monaco offer] is a relatively short contract because Eric is 33 years old. Despite the health problems he's had, he is in good shape. The contract duration will be short but there could be options afforded to the player once we've completed negotiations.
"Negotiations with Monaco will be settled one way or another by next week as Eric has other proposals. We must be respectful to other clubs."
Abidal spent two years at Monaco before leaving for Lille in 2002.