The Brazil international has struggled to make an impact for Hansi Flick's side, managing only a single goal and one assist in 11 league appearances for the German giants.
Costa has missed the previous 11 Bundesliga games and has been sidelined since February 15 after suffering a hairline fracture in his foot.
A report in Birmingham Live suggests that Wolves are ready to place £8.7m on the table in a bid to bring the 30-year-old to the Premier League, a figure which parent club Juventus are believed to favour.
Costa has one year remaining on his contract at the Old Lady but the report also claims that he is in discussions with Juve to terminate his contract early.
Everton are another English club interested in the winger, who will seem to have a choice of clubs to pick from this summer with teams from Saudi Arabia and China also keeping tabs on his availability.
Costa arrived in Turin in 2018 and has made 103 appearances for Juve, scoring 10 goals and registering 21 assists for the club.