The attacker enjoyed the best-goalscoring campaign of his career during the 2022-23 term, helping the Serie A club to their first Italian crown in 33 years.
Osimhen scored 26 goals and provided four assists in 32 league appearances, finishing as the division's top scorer during his third full season since switching from Lille in the summer of 2020.
Having made the net ripple on 20 occasions in as many matches for Nigeria since his international debut in May 2017, the former Wolfsburg man is also a consistent marksmen for his country.
With Osimhen's contract at Stadio Diego Armando Maradona expiring following the conclusion of the 2024-25 term, Napoli president De Laurentiis has provided further insight into the forward's contract negotiations.
"I have never not been calm when it comes to [Victor] Osimhen, but it takes two to tango. I remain the same, if his mood has changed, then there's not much I can do about that," claimed the Napoli chief when questioned on Osimhen's future at the club.
"If after a handshake things change, that is disappointing, we take it into account, but life goes on. We have a good rapport with him, the contract runs to 2025, so there is time. Don't forget that I sold [Kalidou] Koulibaly at the last minute."
As De Laurentiis alludes to, Napoli have not been strangers to selling some of their prized assets during the final year of their contract, with Kalidou Koulibaly moving to Chelsea for £30m last year.
It is understood that Jurgen Klopp's Liverpool are interested in bringing the Nigerian forward to Anfield, and it is believed that the Premier League side have stepped up their due diligence surrounding the player in recent weeks.
Klopp reportedly sent one of his senior scouts to watch Osimhen play for Nigeria against Saudi Arabia in a friendly over the past week - game in which the striker was forced off after 59 minutes due to a hamstring injury.
It is also understood that Chelsea are in the race for the services of the player, with Mauricio Pochettino's side monitoring Osimhen's contract situation in Naples before pressing on with their attempts for his signature.
Some reports are suggesting that the West Londoners are in pole position to sign the attacker in 2024, although the likes of Liverpool and Paris Saint-Germain are set to be contenders for his services.
Following the resignation of title-winning coach Luciano Spalletti and the subsequent arrival of Rudi Garcia, Napoli have struggled to carry any momentum into the new campaign, with the Partenopei currently in fifth place, seven points behind leaders AC Milan.
After sustaining an injury on international duty, it is unlikely that Osimhen will play a part when his side travel to face Hellas Verona in Serie A on Saturday afternoon.