The Italy striker will be handed a pay-rise and an extra year added to his 2017 deal.
"We've received a phone call where we were asked to be patient," Fabio Andreotti told Si Gonfia La Rete on Monday.
"Everything will be sorted out soon and I am convinced that President Aurelio De Laurentiis will make Lorenzo happy.
"I have great faith in De Laurentiis. Last year he made it clear that he wanted to keep Lorenzo at Napoli, whereas we agents wanted him to go and mature at another club.
"Everything is ready and it doesn't matter whether the signature is added before or after the game against Chievo.
"De Laurentiis has always kept his promises and it is his objective to keep Insigne at Napoli for life."
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