According to El Mundo Deportivo, the 23-year-old is disappointed with how he has been treated at Camp Nou and is now looking to leave for regular first-team football.
Belgian side Anderlecht have also shown an interest in signing the youngster, but it has been reported that he has no interest in leaving Spain.
Meanwhile, both Sociedad and Valencia are willing to offer him an escape route from Tito Vilanova's side.
It is believed that La Real hold the advantage in the race as they can offer Champions League football as well as a first-team place.
Dos Santos came through Barca's famous La Masia, but he has been unable to force himself into the first-team setup.