Abidal is available on a free transfer following his release by Barcelona.
He had been offered an ambassadorial role at Camp Nou, but is looking to prolong his playing career on the back of liver transplant surgery.
It is expected that he will return to his native France, with Nice, Lyon and Paris Saint-Germain all linked with his services.
It was, however, Monaco who were believed to be leading the chase for the 33-year-old full-back, but they now appear to be out of the running after leaving Abidal and his representative frustrated.
"I no longer have any news from Monaco", David Venditelli, Abidal's agent, said in L'Equipe.
"The way they handled the case is disturbing, and was up to the limit of being disrespectful.
"Monaco had the opportunity to show that they were not just a club interested in money by taking a free player. They did not do so.
"I respect their sporting choice of not going for Eric Abidal. What I do not accept is the way people are treated."