Sinclair is out of contract in the summer after refusing a new deal at Anfield and the Reds turned down a bid from the Hornets for the teenager in January as it did not meet their £3 million valuation.
Meanwhile, Zielinski is currently on loan at Empoli from fellow Italian side Udinese, the latter of whom are owned by the Pozzo, who also have control of Watford.
The Telegraph claims that the Polish midfielder is a target of Klopp's ahead of the summer transfer window, and that Liverpool are attempting to broker a complicated swap deal.
The Reds are reportedly hoping that Giampaolo Pozzo will allow Zielinski, who is out of favour at Udinese, to join Liverpool in exchange for Watford finally getting Sinclair, a long-term target.
Sinclair is out of contract at Liverpool in the summer, but as the forward is only 19 years old, the Merseyside club are entitled to receive compensation from any club who signs on the youngster.
The Reds are hoping to convince Pozzo to allow them to sign Zielinski rather than going through the potentially lengthy proceedings of agreeing a financial packet, which could require a tribunal if the two clubs were not able to agree a fee.
However, Pozzo will feel that he holds the cards, as foreign clubs are not obliged to pay compensation for signing out-of-contract youngsters in the same way that British clubs must, and so any deal would likely require a great deal of negotiation.