Zielinski has been heavily linked with a move to Anfield this summer.
Jurgen Klopp had reportedly made a £9.5million bid for the Poland international, who has also been linked with moves to Napoli and AC Milan.
However the Reds have struggled to close out a deal for the 22-year-old as he wanted to focus on Euro 2016 before making a decision on his future.
Zielinski’s agent Bartolomej Bolek, suggested earlier this week the player had now decided where he will play football next season.
“It’s true [that Liverpool have been tracking the player for a long time] but I don’t like to talk about negotiations in the papers,” Bolek told.
“We’ve decided, but it’s a secret.”
Liverpool have decided to turn their attention to alternative options after difficulties in negotiations for the midfielder.
The report adds Zielinski is now expected to swap Udinese for AC Milan.
Zielinski has spent the last two seasons on loan at Empoli.