As reported earlier this week, Birmingham-born Deeney is no stranger to transfer speculation - having been linked with a variety of clubs over recent years - and is understood to be keen to remain with Watford and fight for his place in Javi Gracia's starting line-up.
Walsall, who signed Deeney back in 2006 before selling him to the Hornets for £500,000 in the summer of 2010, have an active sell-on clause of around 20%, which, if a deal is eventually agreed, could see them collect some much needed funds with plenty of space remaining in Dean Keates' matchday squad..
30-year-old Deeney has been linked with a variety of clubs over the years including, former Premier League champions Leicester City, West Bromwich Albion, and, most recently, Cardiff City, but the player is believed to be happy to remain with the Vicarage Road club, after settling down with his family.
According to reports on the ESPN website, the Clarets are prepared to offer Deeney a five-year contract as manager Sean Dyche, who is yet to make a signing so far this summer, looks to bolster his attacking options with the club hoping to reach the First Round proper of the UEFA Europa League.
The reports also suggest that the Turf Moor side had been keen to sign West Bromwich Albion striker Jay Rodriguez, but have turned their attention to Deeney after seeing bids rejected.
The reports also suggest that the Turf Moor side had been keen to sign West Bromwich Albion striker Jay Rodriguez, but have turned their attention to Deeney after seeing bids rejected.