Real bounced back from their Champions League semi-final exit on penalties to Bayern Munich by claiming a 3-0 win over Sevilla to move them one step closer to the title.
And their lead at the top of the table will become unassailable should they claim a win at the Estadio San Mames in midweek.
Barcelona thumped Rayo Vallecano 7-0 on Sunday following the announcement coach Pep Guardiola will leave the club at the end of the season, but if Real beat Athletic, the gap at the top will be too big for Barca to overhaul.
Real assistant coach Aitor Karanka believes the Whites deserve to be champions and hopes they can claim the title on Wednesday night.
"It's obviously important to win the Spanish league for everything it entails and for how hard we've worked for it," Karanka told the club's official website, www.realmadrid.com.
"The sooner we win, the better. It would be nice to win at a great venue like San Mames against Athletic Bilbao because they are having a great season.
"Winning La Liga is the objective of every team. Winning such a demanding league championship, which has so many games, is more than important."
"This team deserves to win the title. We're all thinking about winning the game and we need to celebrate as soon as possible.
"Regardless of winning the league title or not, these players have the character and mentality of champions."
Barca were also knocked out at the Champions League semi-final stage by Chelsea last week, and with their title hopes slipping, midfielder Sergio Busquets revealed two other targets for the end of the season, including winning the Copa Del Rey.
Barca will face Athletic Bilbao in the cup final, but first they have three league games left and begin by taking on Malaga at the Nou Camp on Wednesday.
"The most important thing is the team," Busquets told the club's official website, www.fcbarcelona.com.
"We have to do everything we can so that Leo Messi finishes the season as top goalscorer. "He's broken all the records, he's the best in the world.
"Also, the game we have left [cup final] is very important, I hope Pep can leave the club with the cup title."
Sixth-placed Atletico Madrid will be looking to boost their hopes of Europa League football when they take on Real Sociedad on Wednesday, while second-bottom Real Zaragoza face a tough game against Levante in their bid to avoid relegation.
In the other games, Mallorca play Rayo Vallecano, Sevilla take on Real Betis and Valencia host Osasuna.
Getafe's hopes of European football next season appear all but over after they were held to a 1-1 draw by already-relegated Racing Santander.
Granada moved within touching distance of La Liga survival with a hard-fought 2-1 win over Espanyol thanks to two goals from Odion Ighalo.
Villarreal eased their relegation fears and all almost certainly consigned Sporting Gijon to the Segunda Division with a 3-2 win at El Molinon in a match which saw both home coach Javier Clemente and substitute Villarreal goalkeeper Cesar Sanchez sent off.
Wednesday's La Liga Fixtures
Tuesday's La Liga Results