A deal is being worked on to bring the 29-year-old Brazilian in on loan for the rest of the season, with the option – not an obligation – to buy him in the summer.
And it is understood the permanent option would be roughly £17.7m (20m Euros).
Wolves are aiming to boost their strikeforce after Raul Jimenez's injury and a recent poor run of results in the Premier League.
Willian Jose's move is not yet set in stone but on course to be completed.
He scored both goals for Sociedad in a 2-0 Copa Del Rey victory at Cordoba on Wednesday night.
The former Brazil Under-20 international has scored an impressive 52 goals in 143 La Liga games for the Basque outfit.