Jose Mourinho's men have struggled in the league so far this season and are already 13 points short off the table-topping Catalan giants.
However, the veteran is adamant all is not yet lost for the current titleholders, and believes that they could still enjoy a comeback in the second half of the campaign.
"If there's one team that doesn't give up, it's Madrid," the 34-year-old told reporters at a press conference.
"They will fight to the end. This already happened to us two years ago, we were 12 points ahead but had to go to the Bernabeu and win to win the league.
"Mourinho is a great coach and has won many titles. We have to focus on ourselves and forget about the competition. The team have great confidence, we're on fire, and the dynamics of the team are working well."
Regarding a possible contract extension with his club, the Spain international is confident of a positive arrangement, however, also noted that his form will determine how long he will keep playing.
"After my arm injury I focused on recovering. Now I am talking to the club and we are well advanced. I don't think there will be any problems. I want to play but I will not drag down the team, when I do not feel well I will leave regardless of contracts.
"I've been through tough times, the arm injury was bad but now I’m back to enjoy my football. I want to play up until I'm 40."Puyol also stated that his fitness will determine how long he will continue representing La Roja.
"I feel fine, and when the next call comes, I will talk to the coach and if he thinks I'm fit, I will continue. I do not set deadlines."
Puyol has won 99 caps for Spain during his 12-year international career.