The 24-year-old emerged as a shock target late on Monday and discussions are ongoing between the clubs, with Wolves hoping to finalise a deal which would see the midfielder join on loan.
Sanches, who came to prominence at Benfica, has rejuvenated his career in France after difficult spells with Bayern Munich and Swansea.
But he has now emerged as a serious target for Wolves, who are believed to be keen on inserting an option to buy in any deal.
Boss Bruno Lage has been keen to strengthen his midfield all summer but the club’s search had gone quiet in recent weeks.
Sanches is currently sidelined after undergoing knee surgery but while he would not be available to play until the end of September, Wolves still consider the deal worth exploring.
Adding a central defender is also on the agenda, though the chances of bringing in Sanches’ Lille team-mate Sven Botman appear to be fading, due to the Dutchman’s £25million asking price.
Midfield prospect Harvey Griffiths is one player expected to arrive in a £350,000 deal from Manchester City, with the 17-year-old set to team up with the club’s under-23s.
Wolves’ focus heading into the final hours of the window remains very much on incomings with the club unlikely to consider any late bids for Adama Traore or Ruben Neves, both of whom were linked with moves away earlier in the summer.
Striker Hwang Hee-chan became the fifth arrival of the window when he arrived on a season-long loan from RB Leipzig.
The South Korea international has been backed to have a positive impact by defender Romain Saiss, who said: “Every good player who comes to the club, it’s good for us, good for competition between players.
“It is a good point for us to have this kind of player. Hopefully, he is going to help the team.”
Hwang became just the fourth new senior player signed since Lage took charge in June and the head coach has made no secret of his belief the squad needs quality additions.