The La Liga champions were beaten 4-2 at home by Girona in the league on Sunday before suffering a 3-2 loss to Royal Antwerp in the Champions League on Wednesday.
The loss in Spain's top flight left Barcelona in fourth position in the La Liga table, seven points off the leaders Girona, but the club still finished top of their Champions League group despite their latest defeat.
According to AS, Xavi is now facing 'maximum pressure', with none of the club's six board members, including president Joan Laporta and sporting director Deco, believed to be backing him.
The report claims that another poor result against Valencia on Saturday could lead to the 43-year-old losing his job, with senior figures at the club losing faith in him.
After the defeat to Antwerp, Xavi told reporters: «We have to be self-critical, but we are alive. We have to think about where we came from. I think we are much better mentally than last year.
»I consider myself capable of turning the situation around. We have four titles at stake and I am positive. Nothing has changed. I am confident that the team will improve. Trust me. Laporta and Deco have confidence in me.
«It is not a matter of trust, the system gives a lot of confidence, but it is a matter of inspiration. Sometimes wearing a Barcelona shirt can be heavy.
»Today we spent two hours talking with Deco and president Laporta. There is no problem inside. I'm fine, positive. It is not that I am in a bad situation.
«The defeat that hurts us is the one on Sunday in Girona, not this one… we are in the round of 16 of the Champions League after two years.
»All this will
Read on sportsmole.co.uk