According to Mundo Deportivo, Barca are negotiating the 29-year-old's exit after he scored just one goal in 11 appearances for the 19/20 La Liga runners-up.
West Ham and Everton are two clubs who are reportedly interested in signing the forward, whose contract expires in 2021.
Braithwaite has previous experience of English football.
Garry Monk signed him for Championship side Middlesbrough in July 2017 on a four-year deal, but the Denmark international had a falling out with replacement head coach Tony Pulis and was sent out on loan to Bordeaux and then Leganes halfway through the following season.
After a successful loan spell, Braithwaite joined Leganes permanently in July last year and scored eight goals in 27 appearances before moving on to Barca in February.
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Braithwaite’s profile is perfect for the Premier League. He’s fast and he's a fighter.
He would likely play as a second striker or on the wing because he isn’t a 20-goal-a-season player.
He could be a great option for a team who aspire to fight for Europa League places.