Redknapp is looking to bolster his striking options, with Loic Remy still expected to depart Loftus Road this summer despite the collapse of his proposed move to Liverpool.
The Rs boss says discussions over 26-year-old Deeney have taken place between his club and the Hornets, but claims that fellow Premier League newcomers Leicester and Burnley are also in the running.
“He is a player who interests me,” admitted Redknapp.
“The chairman has been talking to Watford, but I think there’s one or two other clubs bidding as well.
“I think Burnley came and made an offer and Leicester too, so we’ll have to wait and see with that one.
“We need four or five good players to give us a squad who are capable of competing.”