Last week, the 29-year-old emerged as a target for the Toffees, with Sam Allardyce eager to bring in new players at Goodison Park during the January transfer window.
However, the Hornets captain said that while Everton's interest was flattering, he was not looking to end his eight-year spell with the Hertfordshire club.
"I have been linked over the last six years with several clubs," he told Sky Sports.
"If they are linked with me then thank you for the compliment but I'm not pushing for anything, I am happy with where I am.
"If we get to the summer and Watford say 'shake hands, we are done', then no hard feelings from me, we have been through a lot, good and bad, for the last eight years. They have stuck by me, I've stuck by them, it's no hard feelings, it's work. It's the nature of the business, I am not going to lose any sleep over it."
The former Walsall striker has started in only five of his 11 Premier League appearances so far this season and has managed to score just twice, compared with a return of 10 and 18 goals respectively in the two previous campaigns.
Deeney's last goal came in Watford's 4-2 defeat at home against Manchester United at the end of last month, which was followed by a draw against Tottenham Hotspur and by another defeat, this time against Burnley, over the weekend.
The series of results mean the Hornets have now gone without a win since 25 November and have slipped to ninth in the table after an excellent start to the campaign. Between now and the end of the year, however, the fixtures list should be kind to Marco Silva's men, who will face four of the bottom nine teams over their next five matches.
On Tuesday night (12 December), the Hornets travel to bottom-of-the-table Crystal Palace and Deeney has warned complacency could cost his side.
"We all know Palace are a good team and playing there is difficult, with the players they have got," he said.
"[Wilfried] Zaha can change a game on its head [...] [Christian] Benteke, [Andros] Townsend, [Yohan] Cabaye, there are so many players that can cause us problems and if we are not on our 'A' game it can be another loss and then people say 'Watford are having a wobble'. So we have to manage expectations outside of the group."