The 33-year-old has outlined his ambition to conclude his playing days at Stade Louis II, while admitting several other clubs are interested in his services
The 33-year-old is currently a free agent after the Blaugrana decided against extending his contract at Camp Nou, prompting the former France international to look elsewhere in his bid to prolong his playing days after battling his way back from a liver transplant.
Speaking to RMC Sport, Abidal explored a number of potential destinations but revealed a desire to finish his professional career with the club where it all began.
"I want to continue playing, but I do not know where. I certainly have some options but nothing concrete," he said.
"It would be nice to end my career in France with Monaco, but this is not a priority for me. Equally I could move to Paris Saint-Germain or remain in Spain.
"It is obvious that ASM is one of the best options out there. Now I have to make the right choice and I will take my time in doing so."
The left-back went on to reveal he had attracted interest from both Olympique Lyonnais and Nice, with both of the club's head coaches, Remi Garde and Claude Puel, keen on luring the defender to their respective teams this summer.
"Returning to Lyon could also be a good opportunity for me," he added.
"I had Remi Garde saying he would be happy to have me at Lyon, but I have not had any contact with [president] Jean-Michel Aulas.
"I also had Claude Puel asking me to come to Nice. That could be a good option, but I don't exclude any club."