The Champions League finalists, who routed Athletic Bilbao 4-1 to lift the King's Cup on Wednesday, have an eight-point lead with three matches left and also hold the head-to-head advantage over their arch-rivals.
"We are taking it one step at a time and on Sunday we'll be looking for the second title," Barca defender Gerard Pique said after their cup final victory.
A disillusioned Real have second place assured but have been battered 6-2 and 3-0 in their last two outings. If they win, Barcelona only need a point from their trip to Real Mallorca on Sunday to complete the job.
The Catalans may have had to put their celebrations on hold last Sunday when Villarreal snatched a 3-3 draw at the Nou Camp, but they still managed to set a new record for the highest points tally in a 20-team top flight, moving on to 86 points.
They are now just four goals short of the record 107 scored in a season by John Toshack's Real Madrid in the 1989/90 campaign.
With first and second all but decided, attention switches to the race for the two remaining slots for Europe's elite competition and the relegation battle.
Sevilla are four points clear in third on 63 and have their hands on the last automatic Champions League qualification place. They visit relegation-threatened Osasuna on Saturday.
UNPREDICTABLE ATLETICO
One of the weekend's most intriguing matches sees fourth-placed Valencia (59) visit the Calderon on Sunday (1900) to play fifth-placed Atletico Madrid (58).
The ever-unpredictable Atletico came from 2-0 down with ten men to beat in-form Espanyol 3-2 last weekend, with Diego Forlan leading the fightback.
The Uruguay striker has scored 27 goals this season, one fewer than the league's top scorer Samuel Eto'o, and goes head-to-head with Valencia's leading marksman David Villa, who has 25.
Unai Emery's visitors were rampant in beating Real 3-0 last weekend but have been hit by suspensions to captain Carlos Marchena and midfielder David Silva.
At the foot of the table, bottom club Numancia host 19th-placed Recreativo Huelva on Sunday with a victory vital for either side if they are to avoid the drop.
Numancia (32), Recreativo (33) and Sporting Gijon (34) occupy the bottom three below Osasuna and safety on 36.
