The outgoing Barcelona defender is being chased by three French clubs, according to his agent, but Claudio Ranieri's side are the most appealing
The full-back, who will be a free agent at the end of June due to Barca having decided not to renew the Frenchman's deal, is being pursued by three Ligue 1 clubs - Olympique Lyonnais, Montpellier and Claudio Ranieri's side.
His representative revealed that the 33-year-old is likely to be given a short-term offer to due to his age but that a return to the club he left in 2002 could be wrapped up withing seven days.
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 made his name as a world class defender at Lyon before moving to Camp Nou in 2007 and his agent accepted that a return to the Stade de Gerland
"Of course, because Eric Abidal is Lyon," he added. "His international career started through playing at Lyon.
"He has a great relationship with the club. There are talks with Lyon and his relationship with the club means there's a chance, but we're concentrating on Monaco at the moment as it's his first choice."
Ventidelli also dropped a major hint that incoming Bayern Munich boss Pep Guardiola was eyeing a move from Abidal but that the France international would prefer to play football back in his homeland.
"There are some clubs in Germany [that want to sign him]," he teased. "There's a close friend and coach who knows Eric well but, again, his preference is to return to France."