Carlo Ancelotti's men began the season in routine fashion by beating top-flight newcomers Cordoba 2-0, only for things to turn sour in their two following fixtures.
Consecutive losses to Real Sociedad and bitter rivals Atletico Madrid has seen Ancelotti come under a little pressure, despite leading the club to their 10th UEFA Champions League title last term.
Defeat at newly promoted Deportivo on Saturday would be a third successive Liga reverse - a run Real have not experienced since losing their last five games of the 2008-09 season.
However, Ancelotti is confident that his side have turned a corner after hammering Basel 5-1 in the opening match of their Champions League defence on Tuesday.
"The team's reaction was good," the Italian commented.
"We played with intensity, we pressured them [Basel] high up the pitch and moved quickly up front. Obviously not all the problems have been solved, but I liked the team's reaction.
"I think the fans will be happy with the match. The team played well, we scored a lot of goals and tried to play as well as we could."
Real's arch-rivals Barcelona have enjoyed a far more impressive start to their season as they look to wrestle the championship back from Atletico.
Luis Enrique's side have won all four of their games so far - three in La Liga and one in the Champions League - without conceding, and they will expect to extend that sequence when they visit winless Levante on Sunday.
Champions Atletico, meanwhile, go into the weekend on the back of a disappointing 3-2 Champions League loss at Olympiakos.
Diego Simeone will again be in the stands due to his touchline ban when Celta Vigo travel to the Vicente Calderon, with the Argentinian hoping for a repeat of his side's performance at the Santiago Bernabeu last week.
Celta, who threw away a two-goal lead against Real Sociedad last time out, have lost each of their last five meetings with Atletico.
Sevilla, who have taken seven points from their three Liga outings so far, face an Andalucian derby at Albert Ferrer's Cordoba on Sunday, while resurgent Valencia will look to continue their unbeaten start at Getafe in Monday's only fixture.
Rayo Vallecano, Almeria and Espanyol are all still hunting for their first wins of the campaign but all have tough games this weekend.
Espanyol host Malaga, while Rayo and Almeria face tricky away trips to Villarreal and Real Sociedad respectively on Sunday.
Friday's fixture sees Liga new boys Eibar head south to Elche, and Athletic Bilbao - fresh from their Champions League stalemate with Shakhtar Donetsk - entertain Granada on Saturday.