The Brazilian has long been linked with a move to Manchester United, but it now looks like a move to Molineux, rather than Old Trafford, is on the cards.
Italian publication TuttoSport report that Costa is being brought in to replace Diogo Jota, who signed for Liverpool last week.
The deal is not yet done, but it is close and Juventus are already eyeing-up replacements for the 30-year-old.
Fiorentina’s Federico Chiesa and Shanghai Shenhua’s Stephan El Shaarawy have been targeted as potential new wide men for the Serie A champions, while Atletico Madrid’s Yannick Carrasco is another possibility.
Costa would represent a significant signing for Wolves, as he brings vast experience of top level competition with him, having played for Juve, Bayern Munich and Shakhtar Donetsk in the Champions League, while also racking up 31 caps for Brazil.
Costa did come off the bench in Juventus’ opening Serie A game of the season, a 3-0 win over Sampdoria, but his game time is expected to be limited unless he leaves Turin.
Reports of a fee vary significantly, with figures from £18m-£37m quotes for the 30-year-old. Certainly it seems likely that Wolves would pay somewhere in the lower end of that price range.