Jurgen Klopp is believed to be a big admirer of the Italy international and was keen to make a bid in the summer.
Arsene Wenger meanwhile has tracked Insigne for some time and reportedly sees him as the perfect replacement for Alexis Sanchez should he leave at the end of the season.
Lorenzo Insigne has reportedly agreed a new deal at Napoli
Jurgen Klopp had reportedly eyed a summer move for Lorenzo Insigne
Insigne currently earns £30,000-a-week at Napoli and wants a huge pay rise to keep him at the Serie A club.
Liverpool and Arsenal can easily offer the 25-year-old a better offer than he is currently on.
But both clubs have been dealt a huge blow in their pursuit of Insigne.
Premier League table based on 2017 results Sat, April 15, 2017
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20. Sunderland (6 points from 12 games) W:1 D:3 L:8 G/D -14
Italian newspaper Il Mattino report that Napoli have reached an agreement with Insigne which will increase his wages to almost £3.4million per season.
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The report claims Insigne will sign a new deal that will keep him at Napoli until 2022.
But the contract will not include a release clause.
Napoli president Aurelio De Laurentiis had reportedly wanted to introduce an £85m release clause but Il Mattino claim that won't be in Insigne's new deal.