Uncapped Deeney, 28, who signed a new five-year deal in the summer, has scored in successive victories over West Ham and Manchester United.
Italian Mazzarri said: "Of course he is international level."
Speaking through an interpreter, Mazzarri added: "I would be proud and really happy if Deeney went to the national team.
"He has improved physically and he is much fitter now. He is a strong striker - he just needs to look after his fitness.
"I respect the England manager and his decision, and I am biased as he is one of my players.
"The FA can call me with the help of an interpreter, but they haven't called up until now."