Deeney has started the new season in red-hot form and his goalscoring exploits have alerted several Premier League clubs.
Tottenham are thought to be actively monitoring his progress at Vicarage Road with Andre Villas-Boas in the market for striking reinforcements, especially if Jermain Defoe and Emmanuel Adebayor leave White Hart Lane.
Fulham boss Martin Jol and his West Ham counterpart Sam Allardyce have both admitted they are looking to bring in a new striker before the close of the transfer window and Deeney is thought to figure highly on their wanted list.
Representatives from Fulham and West Ham are both thought to have watched Deeney in action last weekend when he scored a superb hat-trick in the 6-1 win over Bournemouth.
The 25-year-old is now widely regarded as the best striker outside the Premier League having scored 20 goals last season.
Watford are desperate to keep hold of their prize asset as they look to mount a bid for promotion to the Premier League, but manager Gianfrano Zola admitted after the win over Bournemouth he was wary of clubs making moves to sign Deeney.
Zola, who is a big fan of Deeney and has previously admitted the player could make the step-up to the Premier League, said at the weekend: "The transfer window is still open - and that could be a problem."