Liverpool have been loosely linked with a move for Zielinski in recent months.
The Reds are not expected to splash serious cash in the summer transfer window but manager Jurgen Klopp is expected to spend.
Zielinski could have been a bargain signing from Napoli to strengthen Liverpool’s midfield.
But the Poland international appears happy exactly where he is.
Italian outlet Calciomercato claim to have information that Zielinski is set to sign a new contract at Napoli.
The 24-year-old joined the Naples club from Udinese back in 2016.
And he is more than happy to sign a new contract to remain under manager Carlo Ancelotti.
Zielinski’s new deal would see him extend his stay at Napoli until 2024, Calciomercato report.
They claim Marek Hamsik’s transfer to Chinese side Dalian Yifang this year means Zielinski is convinced he will maintain his place in the first XI.
Yet remaining at Napoli would certainly see Zielinski earn a lot less than he could at Liverpool.
Zielinski is currently on £34,000 a week in Naples.
That is roughly the same wages youngster Joe Gomez was picking up at Anfield before his new contract before Christmas.
Asked about his situation earlier this week, the midfielder said: “I am happy about my condition and I want to continue.
“[Maurizio] Sarri and [Carlo] Ancelotti are different and I want to thank Ancelotti for his trust.
“I can improve and score more goals, I try to improve every day, I want to reach the top.”