According to The Mirror, West Bromwich Albion are interested in signing the striker in the summer and are to make a £20 million bid.
Mazzarri, though, has suggested that he is not planning to part company with the 28-year-old former Walsall star, who earns £65,000-a-week as salary at Vicarage Road, according to The Mirror.
“Why on earth would I want to sell him?” Mazzarri told The Mirror.
“I respect him, he is my captain and my relationship with him doesn't change,” added Mazzarri. “Next season I want two strong players for every position, and if Troy accepts the competition, I will be even happier.
“To take this club to a higher level, we will need 22 strong players, so why would I sell one who has always played for me this season?”
Blow for West Bromwich Albion?
Deeney is one of the best players at Watford and has proved himself to be good enough to play in the Premier League.
The Englishman has scored 10 goals and created 36 chances in 31 league matches for the Hornets so far this season.
During the 2015-16 campaign, the striker scored 13 goals and created 56 chances in 38 Premier League matches for Watford.