The France international was diagnosed with a tumour on his liver in March 2011 and, though that was successfully removed by doctors, the Frenchman required a transplant a year later.
And he has now explained that Alves, who wears Abidal's shirt number for Barcelona this season following his friend's close-season departure, was prepared to make a sizeable sacrifice upon hearing the news.
"My relationship with Dani goes much further than him taking my old No. 22 shirt," he told Radio Catalunya.
"When I had to undergo surgery, he offered to donate his liver. Of course, it’s completely out of the question because he is a professional footballer.
"Our relationship goes much deeper than friendship."
He has started all of Monaco's first five Ligue 1 games this term, and has helped his new club to top spot.
