Los Blancos know that victories over Celta Vigo and Malaga in the final week of the season will give them a first La Liga title in five years.
Barcelona did their best to maintain the pressure by beating Las Palmas 4-1 on Sunday evening, but Madrid recorded victory over Sevilla by the same scoreline in their final Bernabeu outing of the campaign.
Enrique has warned Madrid that they have a couple of tricky assignments left to face, though, starting with Wednesday's trip to Balaidos.
"They have two very difficult games against two teams, Celta and Malaga, who we have lost against this season," he told Movistar. "If we have lost there then anyone can lose there and I want to point out that we have lost in Vigo many times.
"We have one game left and clearly the objective is to win that game, to give us a chance to be champions."
Barcelona host eighth-placed Eibar in their final game of the season, with the top two sides kicking off at the same time next Sunday.