The Hammers are reportedly preparing a $23million (€20m) bid to complete a deal for the 29-year-old.
Braithwaite joined Barca from Leganes in February as an emergency signing, making nine LaLiga appearances and scoring one goal last term.
While Braithwaite's contract runs until 2024, Setien has reportedly told the club the Dane has become surplus to requirements.
As part of the terms of his midseason move, Braithwaite is ineligible for this season's Champions League campaign.
West Ham finished the 2019-20 Premier League season in 16th place.