The 22-year-old Spanish international collapsed after jogging back towards his own goal 35 minutes into the Primera Liga match against Getafe.
Sociedad are thought to be seeking a new coach after current incumbent Juan Manuel Lillo failed to gain promotion back to the Primera Liga.
England captain Beckham was dismissed in the 36th minute of his side's Primera Liga match on Sunday for swearing at a linesman.
The Primera Liga club eventually changed their tack last week by issuing a statement declaring they would not keep Robinho "against his wishes".
Inspired by the brilliance of Cristiano Ronaldo, Real closed to within two points of leaders Barcelona at the top of the Spanish Primera Liga.
Liverpool boss Rafa Benitez has not been slow to visit the Primera Liga, and Torres becomes the 18th import from Spain to pitch up at Anfield.
The Spanish Primera Liga season starts on August 29 with Real bidding to wrest the title back from Barcelona, who completed a memorable treble last term.
After Beckham chose Real, Barcelona bought the Brazilian Ronaldinho, who guided the Catalan club to two Primera Liga titles and the Champions League crown in 2006.
BBC: SPORT | Football | Europe | Beckham exit 'will not hurt Real'
Of his 50 goals this season, Messi has scored 30 in the Primera Liga, meaning he still trails Cristiano Ronaldo by two goals in the Spanish golden boot standings.
The 62-year-old sealed transfers for Zidane, Ronaldo, Luis Figo, David Beckham and Michael Owen among others, to a side that won the Primera Liga twice and European Champions League under his leadership.
Up to 27 Primera Liga players could miss the final league match of the season because of international call-ups for the Nations Cup qualifiers, the Copa America and the European Under-21 championships.
BBC: SPORT | Football | African | Diarra puts Mali above Madrid
Manchester United are the champions of England, Barcelona are the champions of Spain and, by common consensus, the English Premier League and Spanish Primera Liga are the two most glamorous leagues in European football.
Real Madrid's 3-2 reversal against Villarreal on Saturday night handed the Catalan side the Primera Liga crown for the first time since 2006 -- and expectations were high of a showcase of Barca's attacking skills.
Perez is seeking to rebuild a team which finished second in the Primera Liga last season, nine points behind Barcelona, and again failed to progress past the first knockout stage of Europe's premier club competition.
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