The Bluebirds are in danger of suffering the drop following Sunday's 4-0 defeat to fellow struggling side Sunderland.
"I am definitely ready to fight if we go to the Championship," Wales Online quotes Fabio as saying. "I will fight to get us back up if that is the case.
"But we still have two games left and we still believe we can stay in the Premier League. If we do go down, I am ready to battle to get us back up. We can do that straight away, everyone at the club feels the same."
The Brazilian signed a three-and-a-half-year deal at Cardiff when he moved to Wales from Manchester United in January.