The Spanish midfielder signed for Watford in January in a €5.5m deal from Fiorentina, and could be changing clubs for the fourth time in 12 months.
The latest claims in Spain suggest a transfer could be completed quickly, as Plaza Deportiva believe Valencia already have an agreement with the player.
Valencia reportedly have offered the 29-year-old a four-year contract, and the deal has been completely closed.
However, Valencia don’t have agreement with Watford yet, but have opened negotiations with the Premier League club in the past few hours.
Plaza Deportiva say negotiations are on track, and a deal could be completed in the ‘coming days’. Valencia are expected to pay around €5.5m for Suarez.
Valencia boss Pako Ayestaran recently told the Spanish media that ‘Suarez is a proven player’, and it does seem a transfer is likely if all parties can reach to an agreement soon.