Contacted by AFP, a Barcelona court said it had investigated a possible crime of organ trafficking for more than a year before deciding not to proceed because of a lack of evidence.
"FC Barcelona roundly deny any irregularity in the matter," the club said in a statement in English on their website.
Abidal, a former France international, received a liver transplant in April 2012 at the Hospital Clinic in Barcelona and resumed his playing career a year later before retiring in 2014.
On Wednesday morning, online newspaper El Confidencial reported that a telephone tap of former club president Sandro Rosell, suggested that the club illegally acquired a liver for the player.
Rossell is due to face trial on charges of money laundering in connection with Brazilian TV rights sales and was also investigated for the deal which brought Neymar to Barcelona.
Abidal, who is 38, was named Barcelona's sport director in June.
"The club are saddened by the lack of rigour in the spreading of such information about such a sensitive issue," said the Barcelona statement.
The clinic and the Spanish organ donation organisation (ONT) both issued statements denying any wrong-doing, although ONT added that it had opened an internal investigation.
On Thursday July 5th, Abidal published a photo on Instagram of him in hospital with his cousin by his bedside, who El Confidencial claimed hadn't been the liver donor as suggested at the time in the press.
Con la publicación de esta imagen quiero pedir respeto hacia mi primo Gerard y defender su honorabilidad. Denuncio públicamente la actitud de algunos medios que siguen poniendo en duda la legalidad de una intervención que me salvó la vida. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ¡Basta ya! Pido respeto para todos los que hemos pasado o están pasando por una situación similar. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ --------------- ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ With this image, I want to show my respect for my cousin, Gerard, and defend his honour. I wish to publicly condemn the attitude of some media outlets who are suggesting any doubt in the legality of the intervention which saved my life. Stop now! I request respect for myself and everyone affected personally by this stage of my life, and for anyone else in a similar situation. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀