The Citizens chief is already planning his transfer moves for January after watching his new side make a stuttering start to the Premier League campaign.
Despite investing heavily in his attacking ranks by bringing in Stevan Jovetic, Alvaro Negredo and Jesus Navas, the Chilean is still keen to add to his options in the final third.
It is believed that he wants a young player to offer a different option, with Zielinski fitting the bill.
The 19-year-old has already notched three goals for Poland’s senior side, and has broken into the first-team at Udinese.
Pellegrini is preparing to send scouts to assess the teenager further in the coming months ahead of a possible winter bid.
A number of other top European clubs are also monitoring the situation, but City are hopeful that they can swoop early to fend off rival interest.
Pellegrini’s men have made an underwhelming start to the new season, with their two wins balanced out by a shock defeat to newly promoted Cardiff and a disappointing 0-0 draw with Stoke.
Do Manchester City need Piotr Zielinski? Or should John Guidetti be given a chance to impress?
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