Barca still lead the standings with 35 points from 16 games but Real Madrid, on 34, can take their place at the top if they win at Valencia on Sunday.
Barcelona were held to a 2-2 draw at Real Sociedad in an entertaining game on Saturday which could see the leaders knocked off the top of La Liga by Real Madrid by the end of the weekend ahead of Wednesday's 'Clasico'.
Spain international Mikel Oyarzabal gave the home side the lead in the 12th minute from the penalty spot after Sergio Busquets was penalised somewhat harshly for tugging the shirt of Diego Llorente while they battled for an aerial ball.
Antoine Griezmann levelled for Barca in the 38th minute, scoring against the club where he began his career by nonchalantly scooping the ball over Alex Remiro after being played in by Luis Suarez in a sweeping counter-attack.
Suarez put the Catalans ahead in the 49th minute, passing a lay-off from Lionel Messi into an empty net.
Sociedad levelled shortly after the hour mark, as Swedish youngster Alexander Isak pounced on a loose ball and smashed it home from close range.
Barca still lead the standings with 35 points from 16 games but Real Madrid, on 34, can take their place at the top if they win at Valencia on Sunday. Real Sociedad are fourth on 28.