At Sociedad, González put in some good performances, most notably against Real Madrid, against whom he scored Sociedad's equaliser on 8 April as the game finished 1–1. He played 16 league games for Sociedad and scored five goals. Sociedad showed interest in taking him permanently, along with several other La Liga clubs, but González is quoted to have said, "I am very thankful to Real Sociedad and their coach José Mari Bakero, but while they'd like me to stay I'm going to England to join Liverpool."