The Brazilian hitman has slipped down the pecking order at the Estadio Anoeta in the last 18 months and he was loaned to Premier League side Wolves for the second half of 2020/21.
However, after Wolves opted against activating their purchase clause on the 29-year-old, he return to the Basque Country this summer.
His situation remains unsettled with La Real and Imanol Alguacil has confirmed he is willing to sell him for the right price.
Jose reportedly wants a contract until 2025 at the Estadio Ramon Sanchez Pizjuan with his current contract in San Sebastien running until 2024.
Contract demands are the main stumbling block, with Sociedad unwilling to sanction another loan, and Pellegrini angling for a shorter contract length.