Ahead of the long season's final day, Real have a two-point lead over Real Sociedad, who are at home to Atletico Madrid. Both matches kick-off at 1900 GMT.
A Real Madrid draw or defeat would hand the championship to Real Sociedad - provided they win - because of their better head-to-head record.
Real Madrid are desperate to finish the season on a high note after missing out on the Champions League, and the players are unhappy that news of Beckham's move from Manchester United broke as they were preparing for Sunday's decider.
"It's difficult but we have to remember there's an awful lot at stake on Sunday," Real defender Michel Salgado said from the club's training ground.
"We need to be thinking about the game against Bilbao and nothing else. It wasn't the perfect moment to announce the signing of Beckham." Bilbao will be playing for much more than pride on Sunday.
The Basques need the three points to be certain of a UEFA Cup place next season. They will also be eager for a victory to honour the memory of their club president Javier Uria, who died from cancer this week aged 41.
If Bilbao do manage to avoid defeat at the Bernabeu, Real Sociedad can take full advantage with a home win over Atletico Madrid, thrashed 4-0 at home by their Madrid rivals last week.
Sociedad were on course for a third league title, and their first since 1982, until last week's 3-2 defeat by Celta Vigo.
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"It's not over yet," Sociedad midfielder Xabi Alonso reminded Real Madrid this week.
"It's true it's not in our hands any more but we're confident Bilbao can get something at the Bernabeu. They need to win as well to make the UEFA Cup.
The only other side with something to play for on the final weekend are seventh-placed Barcelona, who are two points behind Bilbao in the race for the final UEFA Cup place.
Barcelona need to win at home against Celta Vigo and hope Bilbao manage no better than a draw at the Bernabeu to move up to sixth and clinch the last entry for the UEFA Cup.
Barca's new president Joan Laporta missed out on signing Beckham partly because the club are not in the Champions League next season.
His hopes of signing a player of similar stature will suffer a huge setback if Barcelona are forced to play in the Intertoto Cup over the close season in a bid to make the UEFA Cup by the back door.
All other issues in Spain have already been decided.
Whichever side wins the title, Real Madrid and Real Sociedad will go directly through to the Champions League, with Deportivo Coruna and Celta Vigo going into the qualifiers.
Valencia, last season's champions, are certain to finish fifth, giving them one of the two qualifying places for the UEFA Cup.
Recreativo Huelva, Alaves and Rayo Vallecano have already been relegated, to be replaced by Murcia, Albacete and Real Zaragoza from division two.
