After the Nigerian striker fired his team to Scudetto glory last season, there was much speculation over his future with a hefty price tag placed on his head amid talks to extend his stay in Campania.
Out of contract in 2025, lengthy negotiations in the summer appeared to lead to a breakthrough over a one-year extension that would make him Napoli's highest-paid player.
However, the deal was not signed due to what De Laurentiis described as a "change of mood" from Osimhen.
That prompted reports of a downturn in relations between club and player, until the Napoli president's fresh claims that the deal will be signed imminently after all.
He told reporters at an event in Naples: "With Osimhen, we are about to sign the contract that was pending this summer."
Chelsea are understood to be targeting Osimhen alongside Ivan Toney in their pursuit of a new striker, although they may be happy to wait until next summer to strike a deal.
Reports out of Italy suggested the new contract contains a release clause worth just shy of £130million - but it is not clear when that option comes into effect.
Chelsea have also been linked with Napoli winger Khvicha Kvaratskhelia, who has been tipped to interest Real Madrid and Liverpool. De Laurentiis has dismissed talk of a new contract for the Georgian, whose deal runs to 2027.
The Partenopei chief stated: "Why should we renew Kvara? He has a long contract. There is too much negativity in this city."