The original story came from Corriere dello Sport in Italy and was quickly replicated by English media outlets, suggesting that Klopp is keen on adding competition to his attacking ranks.
While the prospect of signing an expensive soon-to-be 28-year-old in a position that needs little strengthening always seemed unlikely, Klopp conclusively buried the idea that Insigne might be joining the club when he spoke at a press conference on Thursday afternoon.
"We will not sign Lorenzo Insigne. I can say this," the Liverpool boss explained.
"Hes a very good player but we will not sign him. he has a long term contract at Napoli. We will not even try it," he added, referring to Insignes contract expiring in the summer of 2022.
Klopp, unusually for him, comments on speculation. "We will not sign Lorenzo Insigne. I can say this. Hes a very good player but we will not sign him." #LFC
— David Maddock (@MaddockMirror) April 25, 2019
Liverpool have invested heavily in new players over the last two years, paying big money for the likes of Mohamed Salah, Virgil van Dijk, Fabinho, Naby Keita and Alisson. But Klopp has previously spoken about not repeating that this summer and once again stated it is unlikely.
He did not, however, rule out at least some possible deals, with Liverpool needing to strengthen if they continue on this upward trajectory and challenge for major honours again in 2020.
"Will this summer be the biggest transfer window? Probably not," he said.
"But our eyes are always open," he added.
Klopp: "Will this summer be the biggest transfer window of LFC? Probably not. But our eyes are always open."
— James Pearce (@JamesPearceEcho) April 25, 2019
Liverpool saw Manchester City rise to the top of the Premier League on Wednesday night after beating Manchester United at Old Trafford. City now lead the Reds by a point and each club has just three games left. It means that even three more wins might not be enough for Liverpool to claim a first league title since 1990, leaving them hoping that others take points off City instead.