Jürgen Klopp had established the Poland international as a top target but has been frustrated in his attempts to land him, with Zielinski's club Udinese proving difficult to negotiate with.
Reds concede defeat in Zielinski chase
In an attempt to persuade Udinese, Liverpool had inserted a sell-on clause in their deal for Zielinski as well as structuring it so that much of the fee was paid up front, rather than in add-ons.
But Zielinski looks set for San Siro - with the player's agent Bartolomej Bolek telling La Gazzetta dello Sport that he had made a decision on his next club but that they would be keeping it quiet.
However, it is widely understood that AC Milan will be his next destination, having been at Udinese since 2011.
He has spent the last two seasons on loan at Empoli, thriving as a regular in central midfield - making 66 appearances over the two years and scoring five goals.
He made his country's 23-man squad for Euro 2016 but made just one appearance as they beat Ukraine 1-0 in the group stages, with Poland beaten by eventual winners Portugal in the quarter-finals.
With Liverpool also unlikely of sealing a deal for their other midfield target, Borussia Monchengladbach's Mahmoud Dahoud, the club will be forced to look at alternatives should Klopp still wish to strengthen the centre of midfield.
Marko Grujic, who made an impressive goalscoring debut in the Reds' 5-0 pre-season thrashing of Fleetwood Town earlier in the week, is the only midfielder he has added to his squad so far this summer.
Reds still hoping for Chilwell deal
Klopp's other priority is at left-back and he remains intent on bringing Leicester City's Ben Chilwell to the club, though the two Premier League sides have been locked in negotiations since the Foxes rejected an opening £7 million bid last month.
The 19-year-old has yet to make his league debut, but the English champions value him at closer to £10 million because of his clear potential - with Liverpool's first tabled bid having been reported as £5 million upfront with £2 million in additional instalments.
The England Under-21 international impressed on loan at Championship side Huddersfield Town last term, Klopp's close friend David Wagner - part of his backroom staff at Borussia Dortmund - recommending Chilwell to the club.
The defender has entered the final year of his contract in the East Midlands, meaning Liverpool could potentially wait 12 months for Chilwell to become available on a free transfer.
But they would still be required to pay a compensation fee for the player, due to Leicester's investment in Chilwell's development over the years, with an independent tribunal then needed to decide said fee.
However, with Chilwell reportedly keen on a switch to Anfield for more regular playing time - and Liverpool willing to wait if they can't persuade Leicester to drop their asking price, they could opt to hold off.
If a deal can't be negotiated, Liverpool younsger Brad Smith could be used as back-up to Alberto Moreno in the coming season - with Klopp having turned down a number of loan deals from Championship clubs for Smith in recent weeks.
Plenty of outgoings are also still expected as Klopp trims the numbers of his first-team squad. Having sold Jordon Ibe, Martin Skrtel and Sergi Canos last week, Luis Alberto and Christian Benteke could officially be let go in the coming weeks.
The Reds are also reportedly willing to listen to offers for winger Lazar Markovic, who has so far failed to take his opportunity in pre-season - although he only played 45 minutes against both Tranmere Rovers and Fleetwood.
Klopp is also keen to sell Mario Balotelli, having told the striker himself that he has no part to play in his plans, though no offers have yet been received for the Italian outcast.