Deeney, who scored 20 times for the Hornets last season, has begun the new campaign in explosive form netting a hat-trick last week in the 6-1 demolition of Bournemouth.
However the Watford boss is confident that the striker will stay at the club and insisted no bids have been made from the Premier League.
"There have been no bids as far as I know," Zola told the Watford Observer.
Deeney, who signed a new three-year deal at Vicarage Road in March, was watched last weekend by scouts from both Fulham and West Ham.
Tottenham manager Andre Villas-Boas is currently weighing up a bid for the 25-year-old as he looks to add to his attacking options.
Villas-Boas broke the club's transfer record earlier this month with the £26m signing of Valencia striker Roberto Soldado.
Deeney has been identified as a possible replacement for Jermain Defoe, whose future at White Hart Lane remains uncertain with QPR boss Harry Redknapp keen to acquire the forward.