Deeney has been attracting interest from Aston Villa, Newcastle, Everton and Swansea.
The 27-year-old striker, who fired the Hornets to promotion from the Championship last season, is captain at Vicarage Road, and losing him before the start of the season would be a big blow to their hopes of staying in the top flight.
The Mirror has reported that Everton want to sign the forward, whilst the Daily Mail has reported on interest from Newcastle United and Swansea. The Mirror also suggested that Aston Villa are tracking Deeney, who started his career as a trainee at Villa Park.
Deeney has netted 66 goals in the last three season, scoring at least 20 per campaign, and his prolific record and leadership abilities have made him an in demand striker target.
He only signed a new contract last summer, agreeing a four-year deal, but the forward is set to be offered a new deal as the Hornets prepare for their first Premier League campaign since 2006/07.
This deals a blow to all the Premier League sides interested in signing the striker, and gives great hope to Watford that survival is a real possibility this coming season.