The 20-year-old defender agreed to join Athletic Bilbao on a season-long deal over the summer, but has grown frustrated at a lack of opportunities in his homeland.
He has been awarded just seven minutes of action this term and feels he needs to explore other avenues.
Reports suggest two Premier League clubs have expressed an interest in San Jose's services and his agent admits an agreement could be struck in January.
"His patience is being pushed and if nothing chances he will leave Bilbao in the New Year," said Jesus Medina.
"We do not understand Bilbao's persistence to strike a deal over the summer if they had no plans to play San Jose.
"This situation is damaging to his career. He is a professional and does not want to cause controversy, but he is suffering at the moment."
Speculation suggests that Blackburn and Wolves are the two English clubs keen on securing a loan deal for San Jose.