The club are working to bring the 29-year-old frontman in on loan from Spanish La Liga outfit Real Sociedad until the end of the season with an option to buy as part of the deal.
Jose, a former Brazil under-20 international, has scored six goals from 21 appearances this season and 62 in 170 games for the Basque outfit overall.
The forward scored a brace during Sociedad's 2-0 win over Cordoba in the Copa Del Rey on Wednesday.
The loss of star striker Raul Jimenez to a fractured skull had left the Molineux men short of experienced options up front and thrust teenager Fabio Silva into the spotlight.
Silva has netted twice this season but the club view the £35m signing as a long-term project.
Boss Nuno Espirito Santo had made it clear he needed to ‘rebalance’ his squad in the transfer window, but with Wolves struggling to make a breakthrough in the market, they recalled Patrick Cutrone from his loan spell with Fiorentina.
However the recent run of poor results, culminating in Saturday’s painful derby defeat to Albion, has seen Wolves redouble their efforts to add a striker.
Jose is understood to have been on Wolves’ radar for sometime and has attracted interest from clubs across Europe.
New Brexit rules may delay the signing process slightly, but Wolves are keen on sealing the move as soon as possible.
Jose started his career in Brazil with Barueri, and had spells at Sao Paulo, Gremio, Santos, Real Madrid (loan), Real Zaragoza (loan) and Las Palmas before signing for Real Sociedad.
His pending arrival would cast doubt over the future of Cutrone, who has been linked with a move to Parma – and would be free to make a move, as players are now allowed to play for three clubs over the course of a season.
Nuno has admitted that his current living arrangements are not ideal, with the 23-year-old living on his own out of a hotel.