According to RMC, Abidal has already been ruled out of Euro 2012 and there are doubts over whether he will ever be able to return to competitive football after the procedure.
However, Benzema is hoping for the best for a player and a person he holds in the highest esteem.
"I hope this is not very, very serious," the Real Madrid striker told L'Equipe. "He's like a brother to me.
"And I do not need to talk about what Eric Abidal is like on the field. He is a truly great player. In his position he is one of the best in the world. I hope he can soon return to football."
Meanwhile, Zinedine Zidane, a former international colleague of Abidal's, is in no doubt that the 32-year-old Barcelona defender will return stronger than ever.
"I know him very well," the World Cup winner is quoted as saying by RMC. "I played a lot with him.
"It's always a tough fight but I know he'll come through it. I just want to tell him to have courage. It is the most important thing for him and his family."
Abidal had a tumour on his liver removed last year and battled his way back in time to lift the Champions League trophy in May.
Since November, Goal.com has been publishing exclusive extracts from Graham Hunter's highly-anticipated new book, 'Barca: The Making of the Greatest Team in the World'. The very last extract, which was published last Friday, looks at Andres Iniesta's risky return from injury in the 2009 Champions League Final and how he was described by Wayne Rooney as the 'best midfielder in the world'. Don't miss it!