According to ESPN, the Clarets offered Watford £9m for Deeney, whom they wanted to sign on a five-year deal.
In addition, according to Sky Sports journalist Adam Leventhal, the Hornets have decided not to sell their captain, despite his failure to impress last season.
Understand #WatfordFC turned down offer of £9m for Troy Deeney from Burnley & won’t entertain more. Looks like they’ve a player coming into season determined, focused & not having had injury disrupted pre-season— Adam Leventhal (@AdamLeventhal) August 3, 2018
Sure he & they want return to form of 1st 2 PL seasons of 15 & 10gls
The 30-year-old has scored 28 Premier League goals for Watford in three seasons in the top flight, but only five of those goals came last season, as he struggled for form and fitness.
Nevertheless, Deeney's experience and leadership skills are clearly still valued by manager Javi Gracia. The Watford skipper has also given promising displays in pre-season matches, as has fellow striker Andre Gray.
Both forwards were significantly under par last season, so Hornets fans will no doubt be encouraged by their bright pre-season form. Nevertheless, they will likely also be disappointed with their club's failure to reinforce their attacking options - especially after the sale of Richarlison to Everton.
Despite his struggles last season, Burnley weren't the first club to be interested in Deeney this summer. Newly promoted Cardiff City also considered making a bid for him, but their interest subsequently waned.
Clarets manager Sean Dyche will likely be disappointed that he will not be reunited with Deeney, whom he managed during his spell at Vicarage Road. Dyche had hoped to reinforce Burnley's attack, which was a major area of weakness last season - the Clarets netted just 36 Premier League goals, which is less than one strike per game.
Unlike Burnley - whose exceptional defence enabled them to finish seventh in the table - Watford showed alarming weaknesses at both ends of the pitch last season, scoring just 44 league goals, conceding 64 and finishing in 14th place with 41 points - just eight more than 18th-placed Swansea City.