ESPN claim new Everton boss Sam Allardyce will make Deeney his number one transfer target for the January transfer window.
The Toffees are still looking for a new striker, having failed to replace Romelu Lukaku's goals since his summer departure to Manchester United, and Deeney was on their radar last summer.
Former manager Ronald Koeman reportedly vetoed any move for the 29-year-old, but Everton director of football Steve Walsh remains a keen admirer of the striker having tried to sign him for Leicester City during his time at the King Power Stadium.
Watford won't want to part with their captain midway through the season, but Deeney himself could be open to a move while he remains down the pecking order at Vicarage Road.
The skipper has made only four Premier League starts this season.