Reports claimed earlier this week that Tony Pulis had placed Deeney at the top of his wishlist for the off-season, looking to capitalise on a supposed falling out between the club captain and his manager.
Deeney claims that his long-term future is down to the Hornets, however, telling reporters: "Leicester, West Ham, Everton - I've been linked with everyone at some point. I'm used to it now.
"I just leave it all to the club. If Watford want to keep me, then I'm happy to stay. If they want to get rid of me, then we will shake hands like men and move on."
Deeney has scored 10 goals in 31 Premier League appearances for Watford this term, leaving him three behind last season's tally.