The Celta Vigo boss is the favourite to take over at Barca should the club decide to dispense with the services of Gerardo Martino at the end of the season.
Reports in Catalonia suggest Enrique met with Barca sporting director Andoni Zubizaretta over the weekend and, should Barca opt to turn to the former Spain midfielder, who played for the Blaugrana and Real Madrid in a distinguished playing career, it would be a move endorsed by Soriano.
"Barca now need a coach with character and clear ideas," the Red Bull Salzburg striker told SER.
"And everyone knows that Luis Enrique does not lack them. Enrique knows how to deal with big players. At first when he was at Roma, he clashed with [Francesco] Totti, but then impressed him.
"He wants possession but, in the end, the goal is what matters. This is what we are seeing at Celta: control of the ball but attacking."
Enrique started his coaching career with Barca B before moving on to Roma and then Celta.