Since moving to Naples in 2016 for a fee in the region of €16m, Zielinski has established himself as a club legend.
A total of 50 goals and 46 assists have been contributed in 343 appearances in all competitions, the Poland international playing a key role in last season's Serie A title triumph.
However, Zielinski is now well into the final year of his contract at Stadio Diego Armando Maradona, putting teams on high alert regarding a potential free transfer.
Last week, it was claimed that each of Barcelona and Inter Milan were each monitoring the situation as they assess the possibility of acquiring the services of the versatile 29-year-old for nothing.
Sporting director Mauro Meluso has since insisted that both parties are working towards signing a contract extension, rather than the player pushing to take a new challenge.
Nevertheless, while he remains without a fresh deal, Zielinski will naturally stay as a transfer target for a wide array of clubs around Europe.
According to Corriere dello Sport, Liverpool and West Ham are among the latest clubs to highlight Zielinski as a possible addition.
From the perspective of Liverpool, they have just spent the summer transfer window signing several different midfielders with contrasting qualities.
That said, Zielinski would act as another experienced head and also provide backup on the left-hand side of the pitch if required.
Meanwhile, West Ham have also invested heavily in the engine room with Edson Alvarez and James Ward-Prowse each establishing themselves as first-choice picks.
David Moyes arguably requires another option, though, to compete with Tomas Soucek, the preference this season having been to move Lucas Paqueta out to the left-hand side.
The report adds that Juventus - who have had well-documented issues off the pitch and with FFP - would be interested in tempting Zielinski to Turin.