The midfielder is currently on loan at Empoli and has earned rave reviews in Serie A this season as scouts have flocked to see him in action.
Liverpool have been monitoring the 21-year-old all season, while Roma were keen on a move during the January transfer window.
And now, according to La Gazzetta dello Sport, the two clubs are ready to go head to head for Zielinski this summer.
Udinese had planned to integrate the Poland international into the first-team squad when he returns from his loan at Empoli.
But, the Italian club are aware of the growing interest in Zielinski and will now consider selling him if someone splashes out over £15m.