Fellow Premier League newbies Burnley and Leicester have also been linked with the 26-year-old, however their bids for him are believed to have been dismissed.
The Hornets are said to be willing to sell to a top tier side, but only if their £10m valuation is met.
Deeney netted 25 goals in all competitions last term, and with fellow Championship stars Ross McCormack and Leo Ulloa having both been sold for £11m and £7m respectively, the Londoners believe that their demands are realistic.
Harry Redknapp is known to be in the market for a forward with Loic Remy’s imminent exit due to leave him with only Bobby Zamora and Charlie Austin as options in the final third.
But it remains to be seen as to whether or not ‘Arry will be keen to pay Watford’s full asking price.
QPR have already moved for Rio Ferdinand and Steven Caulker, while reports today have linked them with French playmaker Mathieu Valbuena.