Widespread reports have claimed that Liverpool value the player in the region of £80m, but the Catalan giants are believed to have fallen short of that figure with a £70m opening offer.
Liverpool are said to be keen on including Alexis Sanchez in the deal, but it remains unclear whether the Chile international wants to move to Anfield.
According to Spanish newspaper AS, Suarez, who scored 31 league goals for Liverpool last season, has verbally agreed to become a Barcelona player.
Should Suarez complete the move, he will miss the start of the season as he serves a four-month ban for biting the shoulder of Italy defender Giorgio Chiellini at the World Cup in Brazil.
Numerous reports have claimed that talks between the two clubs have been 'productive and amicable'.