Wednesday's 1-0 UEFA Champions League win over Basel was their 15th successive triumph, with Cristiano Ronaldo netting his 26th goal of the campaign to seal top spot in Group B.
Real have twice achieved 15 straight wins in the past - in the 1960-61 season under Miguel Munoz and in 2011-12 when Jose Mourinho was at the helm.
And three points at La Rosaleda would give the bulk of Carlo Ancelotti’s team that claimed La Decima - a 10th European title - in May another prestigious entry into Real's catalogue of phenomenal achievements.
Javi Gracia's Malaga were enjoying a purple patch of their own, five consecutive La Liga wins having fired them up the standings, before Real's city rivals Atletico Madrid beat them 3-1 in the capital last weekend - a game that saw both team finish with 10 men as Samuel and Gabi each collected a pair of bookings.
Atletico captain Gabi will therefore be missing when the champions host lowly Deportivo La Coruna in Sunday's early kick-off.
Second-placed Barcelona, meanwhile, are set for a stern examination of their Liga title ambitions when they travel to a stuttering Valencia on Sunday.
Luis Enrique's side head into the 13th round of fixtures two points adrift of leaders Real Madrid at the summit but appear to have emerged from a difficult spell, with Lionel Messi predictably to the fore.
Barca's superstar talisman netted a hat-trick in the 5-1 demolition of Sevilla last weekend, becoming La Liga's all-time record goalscorer in the process.
Messi repeated the dose on Tuesday night, leaving APOEL after a 4-0 Champions League win with the match ball and the distinction of also being the competition's leading marksman.
If fourth-placed Valencia can stop Messi and co in their tracks they could close to within a point of Barcelona, although following a goalless draw against Athletic Bilbao before the international break with a 2-1 loss at Levante last time out has checked their early-season momentum somewhat.
Real Sociedad welcome fellow strugglers Elche on Friday evening as the second match of David Moyes' reign in San Sebastian kicks off the weekend action.
Sociedad will aim to end an unusual quirk of their season so far, where their only two La Liga wins have arrived against the high-flying Madrid clubs.
Granada are only a point better off in 15th and face a tricky assignment at fifth-placed Sevilla.
Like Valencia a place and point above them, Sevilla are aiming to bounce back from two winless encounters, while Joaquin Caparros' Granada have drawn three of their last four but have not tasted victory since mid-September.
Elsewhere on Sunday, basement boys Cordoba welcome Villarreal, who sit eighth having claimed a first league win in four attempts against Getafe a week ago.
Getafe entertain Athletic Bilbao in Saturday's early match, while Espanyol and Levante clash in something of a six pointer before another team looking anxiously over their shoulder, Eibar, travel to Celta Vigo.
Almeria close out the week's fixtures with a home game against Rayo Vallecano on Monday.
