Traore is expected to become a Wolves player on Tuesday, with Tony Pulis' side expected to pocket £18m for his services.
However, that move will leave the Championship side significanlty short of quality on the flanks, something they hope to remedy by bringing in Bolasie.
The 29-year-old is surplus to requirements under Marco Silva, who has Theo Walcott, Ademola Lookman, Richarlison and the in-coming Fred to count upon as options out wide.
Boro boss Tony Pulis knows Bolasie well from their time together at Crystal Palace and he is hoping that bond will be enough to convince the DR Congo star to make the move to Teesside.
Middlebrough have money to spend following the departures of Ben Gibson and Patrick Bamford and are thought to be hoping to agree either a £15m permanent switch or an initial loan move with a view to a £15m transfer in Janiry, depending on whether they can beat Thursday's transfer deadline.