Both sides are owned by the Pozzo family, who regularly loan or sell Udinese players to the Championship team.
Zielinski has already made 15 Serie A appearances, providing two assists, despite the fact he’s only 19 years old.
The trequartista – a creative midfielder who sits behind the strikers – is a senior Poland international with three goals in just five caps.
However, he has struggled for playing time since Udinese went out of the Europa League in the play-off stage.
According to TMW, Zielinski could be loaned to Watford in January so that he can continue his development by playing regularly.
Udinese hope it will also raise his price-tag, as it already did for former Watford loaner Matej Vydra.