Leicester, QPR and Burnley have all been linked with the 26-year-old, who has scored 43 league goals in the last two seasons.
But Watford are standing firm over their asking price for Deeney, thought to be £8million, and have rejected the highest offer of £7.5m from Leicester.
QPR boss Harry Redknapp has admitted his interest in the former Walsall player, although he is waiting for Loic Remy’s future to be resolved before making an offer.
The Frenchman’s move to Liverpool collapsed last week, leaving Redknapp with an extra striker and he might end his interest in Deeney if Remy decides to remain at Loftus Road.
Redknapp told getwestlondon.co.uk: “Troy Deeney is a player we are interested in, but there is nothing happening at the moment, and I don't know if we will pursue it or not.
“We will have to see what happens with Remy, and we need to know whether he's staying or not as we can't have just two strikers, and we can't be suddenly losing him on transfer deadline day.
“We have to make sure we're prepared. If he's staying, we need to get Remy fit, and we've still got two weeks to do that.”
If Watford do not receive an improved offer Deeney is expected to feature in Saturday’s opening Championship match against Bolton at Vicarage Road.