The Catalan giants want to negotiate a loan deal with an option to buy the Spain winger for around £29million.
There is work still to be done on any deal but Traore could return to the Nou Camp seven years after leaving.
It also signals an end to Tottenham’s interest after they had a £15million bid rejected earlier this month.
Spurs are not expected to revive the deal in a blow to Antonio Conte’s hopes of adapting Traore as a wing-back and just earlier this week they remained confident they could sign the 26-year-old.
Traore started his career at Barca before moving to Aston Villa in 2015 and then spending two years with Middlesbrough.
He signed for Wolves for a then club record fee of £18million in 2018.
The club had opened negotiations over a new deal last year but no agreement has been reached and Traore has 18 months left on his current contract.
He has made 154 appearances, scoring 11 times for Wolves, while he made four appearances for Barca, scoring once, at the start of his career.