Real could close that gap to seven when they travel to the Camp Nou for El Clasico on Saturday, and Bale has refused to give up on the chase until it is mathematically impossible.
"I think everything is possible in football. We're ten points behind, but we will keep fighting until it is impossible," he told reporters.
"We have to score there. We know it will be difficult and we will have to be at 100%. You have to attack them and, if we play our best football, we will win.
"On Saturday we can get to within seven points of them and you never know what might happen next."
Barcelona go into the match on a Spanish-record run of 39 matches unbeaten.