The 22-year-old has emerged as their top target in their chase for a new forward this summer.
Traore is believed to have an £18million release clause written into his contract, but Wolves don't believe that figure represents Traore's value.
They face a fight for his signature with several clubs interested including Huddersfield Town, who want Traore as a replacement for Tom Ince who they sold to Stoke City last week for £10m.
It's understood that if Traore does move to Molineux it will not pave the way for Ivan Cavaleiro to leave the club.
Speculation has surrounded Cavaleiro's future all summer and Wolves rejected a £12m bid from Fulham in June.
The 24-year-old wasn't involved at the weekend when Nuno Espirito Santo's side lost 2-1 at Championship side Derby County.
However it's believed he was sidelined with a knock and remains in Nuno's plans.
Traore suffered a dislocated shoulder during Middlesbrough's abandoned friendly against Sunderland on Friday but that hasn't lessened Wolves' interest in a player who scored five goals and provided 10 assists in 40 appearances last season.
He began his career with Barcelona before joining then-Premier League Villa in 2015 for £7m.
Traore left Villa Park a year later without making a league start. He joined Boro for an undisclosed fee with Albert Adomah going the other way and was their star player when they reached the play-offs last season.
Boro boss Tony Pulis said on Friday when asked if Traore's release clause had been met: "No, not at the moment.
"I think everybody, especially me, wants him to be here.
"But we have to do what we have to do, he has a clause, I think everybody knows he has a clause in his contract and if that money is reached it's almost taken out of the club's hands.
"But I've got great respect for the boy and everybody here is hoping and praying he stays.”