Carlo Ancelotti's men kicked off their Liga campaign with an underwhelming win at home to Cordoba and a massive improvement will be required if they are to triumph at the Anoeta
With limited time remaining in the transfer window, Santiago Bernabeu bosses allowed Di Maria to leave for Manchester United and Alonso for Bayern Munich in midweek.
The pair had formed a key part of Madrid's successes in recent seasons, but coach Carlo Ancelotti still boasts a wealth of options at his disposal.
Ancelotti's men opened the league season with a 2-0 win over Cordoba on Monday courtesy of goals from Karim Benzema and Cristiano Ronaldo.
However, they were far from their fluent best and were forced to stand firm amid plenty of pressure from the visitors after the break.
The European champions will be hopeful of finding their attacking rhythm at the Anoeta - a place where they have not lost since the 2003-04 campaign.
Sociedad has struggled against Ancelotti's side recently, with Madrid putting nine goals past it last term.
Furthermore, the hosts go into the fixture off the back of a Europa League exit - Jagoba Arrasate's side suffering a 3-1 aggregate defeat to Russian outfit Krasnodar.
In a week where Madrid learned its Champions League group opponents, Arrasate's men surrendered a one-goal lead to bow out of Europe courtesy of a horror show late on at the Kuban Stadium.
Three goals in the final 19 minutes ended Sociedad's hopes of progressing to the group stages, but Arrasate hopes to see a reaction from his charges when Madrid comes to town.
"The result gives us a lot of sadness and anger. It’s a hard blow but it will make us stronger," Marca quotes him as saying.
Sociedad has no fresh injury concerns although it could still be without Alfred Finnbogason, Ion Ansotegi and Jon Gaztanaga.
Carlos Vela may make his full return, having come off the bench against Krasnodar on Thursday.