Valverde faces an uncertain future at the Nou Camp following the club’s Champions League exit against Roma, although they are on course for a domestic double after beat Sevilla in the Copa del Rey final on Saturday and remain 12 points clear at the top of La Liga.
Don Balon have claimed that Nou Camp chiefs were already eyeing up potential replacements just in case their La Liga rivals emerged victorious at the Wanda Metropolitano.
According to the Spanish publication, Blues boss Conte was one of leading names being considered over the potential vacancy.
But Valverde appears to have eased the pressure on his job after Barcelona thumped Sevilla 5-0.
Antonio Conte has been tipped to leave Chelsea at the end of the season after a disappointing campaign at Stamford Bridge but he still has the FA Cup final to come.
The Italian boss has been in conflict with the club’s hierarchy throughout the season over their dealings in the transfer market.