Los Blancos head into Saturday’s highly-anticipated El Clasico clash 10 points behind their perennial rivals, and with just eight matches left this campaign, it will take a mammoth effort for the Galacticos to chase down the reigning La Liga champions.
Yet Bale feels nothing yet is set in stone and vows to continue fighting for the League trophy.
"I think everything is possible in football,” he said. “We're 10 points behind, but we will keep fighting until it is impossible.
"We have to score there. We know it will be difficult and we will have to be at 100 per cent. 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."
Bale could surpass his best total of 15 League goals for Madrid if he scores this weekend, with the Welsh international admitting he is feeling more at home in the Spanish capital as he looks to continue scoring alongside his star-studded teammates.
"I feel more comfortable here now," he said. "I speak some Spanish. I think I have to keep working hard and improving, giving my all and helping the team.
"Everyone knows I like to play in the middle and then move about, but if I start from out right I can play more economically and support my team-mates better."
Kick-off at Camp Nou on Saturday is set for 20:30.