The Frenchman, who underwent a liver transplant last year, made his return to competitive action at the weekend, ending a 14-month long road to recovery
Abidal was forced to undergo a liver transplant last year but, having made what has been described by doctors as a miraculous discovery, he is back playing again.
The Frenchman came on as a late replacement in Saturday's 5-0 Liga success over Mallorca.
Consequently, Vilarrubi believes that the defender's remarkable recovery warrants recognition.
"Abidal is my candidate for the [Prince of Asturias] Award," the Blaugrana director told reporters on Tuesday. "Honestly, I cannot imagine another who deserves it more."
The prestigious accolade was last year bestowed upon Barcelona midfielder Xavi and Real Madrid goalkeeper Iker Casillas.