Barca's new manager Ernesto Valverde is believed to be keen to activate Deulofeu's £10.5m buyback clause this summer.
The Spaniard joined Everton in a permanent deal in 2015 after coming through the Catalan giants' academy and struggling to break into the first team.
Reports have claimed that Barcelona want Deulofeu back, but the player himself is uncertain due to concerns that he will get limited game time.
According to Mundo Deportivo, agent Gines Carvajal is unhappy with reports regarding the La Liga club's keenness to re-sign Deulofeu.
It is understood that the 23-year-old is open to offers from other clubs.