Mazzarri, who has been out of work since leaving Inter Milan in late 2014, previously managed Hornets pair Miguel Britos and Valon Behrami at Napoli.
The 54-year-old has reportedly received English lessons in preparation for a move to the Premier League, where Swansea City, Sunderland and Liverpool have all been linked with his services in the past.
Watford, who were promoted to the top flight as Championship runners-up a year ago, have won four league games since the turn of the year and, according to the Mail, the club's Italian owners believe they should have made more of their promising start.
And that, it is claimed, will signal the end of Flores' season-long stay at Vicarage Road, despite the Spaniard having achieved what Graham Taylor and Aidy Boothroyd could not - keeping the Hornets in the Premier League.
The former Atletico Madrid coach has been linked with a return to La Liga at Valencia, where Pako Ayestaran is currently acting as manager following the sacking of Gary Neville.