Maurizio Sarri's side must win at Feyenoord and hope Shakhtar Donetsk lose to Group F winner Manchester City on the final matchday of the group stage.
But Napoli will be without Insigne for the game at De Kuip, the Italy international having been ruled out with an injury sustained in Saturday's 1-0 league defeat at home to Serie A champion Juventus.
Insigne has started each of Napoli's 22 matches in Serie A and the Champions League so far this season, contributing four goals in each competition.
Napoli left-back Faouzi Ghoulam is also out of the Feyenoord match with a cruciate ligament injury sustained in his team's Champions League defeat against City last month.
But Napoli announced on Wednesday the Algeria international, reportedly a target for Pep Guardiola, has signed a new contract running to 2022.
"Proud and happy to be part of this great project," Ghoulam posted on Twitter. "To represent this beautiful city and its colours. Proud to be Neapolitan. #ForzaNapolisempre."