The 27-year-old finished as the top scorer in the Premier League last season with 31 goals.
Barcelona have reportedly made a £30m offer for the forward, which includes Alexis Sanchez as a makeweight.
According to Catalan paper Sport, Suarez has stated his desire to quit Liverpool for the Primera Division side.
The Uruguay international is said to have spoken to confidants on the phone while at the World Cup in Brazil to reveal that he has his heart set on a move to Camp Nou.
Suarez joined Liverpool from Ajax in 2011.