With Barcelona and Atletico Madrid, currently first and second, both playing Sunday, Carlo Ancelotti's side could overtake them - for 24 hours at least.
Madrid have tightened up defensively with six successive clean sheets in domestic competitions since the mid-season break and four back-to-back league wins have seen them close the gap between them and Barcelona to just a point.
"We are in a good position. In the league we have cut distances and have to continue this hot streak," defender Alvaro Arbeloa told realmadrid.com.
"Playing first is good to put them under pressure. Let's see if we can win and keep putting pressure them.
"We are in an upward trend and are we doing things right."
By the time Barcelona take to the Nou Camp pitch to face Malaga late on Sunday they could also have been overtaken by Atletico, who kick-off at next-bottom Rayo Vallecano a couple of hours earlier.
Winger Cristian Tello enters the game full of confidence after a hat-trick against Levante in the Copa del Rey on Wednesday - courtesy of three assists from Lionel Messi.
"Scoring a hat-trick gives you a lot of confidence. I'm very happy because opportunities should be taken advantage of," said the 22-year-old, who gave the credit to Messi's delivery.
He added on fcbarcelona.com: "He put me through in front of goal three times and I have to thank him for that.
"It is a play we are used to because he's left-footed. To have a player like that on the team is spectacular."
Coach Gerardo Martino feels Messi is getting back to his best form after almost two months out with a hamstring injury and believes the player is fully focused on his club duties and is not holding himself back for this summer's World Cup.
"He's prepared himself to come back to Barca in the best way possible. He's not preparing for the World Cup, it's not possible to do that," he said.
"What Messi has done is take advantage of his time off the pitch to recover and to prepare himself physically."
Athletic Bilbao travel to mid-table Osasuna looking to consolidate their fourth place with main rivals Villarreal heading to Real Valladolid on Saturday.
Eighth-placed Espanyol will look to hold off the challenge of Valencia by avoiding defeat at the Mestalla while Sevilla host Levante.
In Sunday's early game struggling Almeria are at home to Getafe.