The Nigeria international was inevitably linked with a summer exit from the Partenopei after firing them to the Serie A title with 26 goals from 32 games last year, taking home the Capocannoniere in the process.
All of Manchester United, Chelsea, Real Madrid and teams in Saudi Arabia were believed to be battling for Osimhen's signature, but they were priced out of a move for the former Lille man.
Napoli still have Osimhen under contract until the summer of 2025, and the Italian champions were working to tie him down to an extension over the summer, but an agreement could not be reached.
During a recent interview with Sport Mediaset, De Laurentiis suggested that the pair had shaken hands on a renewal, but Osimhen proceeded to change his mind, and the Napoli president hinted that he would be prepared to sell the striker next summer, citing Kalidou Koulibaly's move to Chelsea as a similar example.
"I have never been unhappy towards Osimhen, but there are always two of us in these things. I have remained the same, if his mood has changed I can't do anything about it," De Laurentiis said.
"If things change after a handshake, it's disappointing, we take note of it but then life goes on. There are excellent relations with him, the contract expires in 2025, there is time. Don't forget that I sold Koulibaly a year before his contract expired."
Despite De Laurentiis's affirmations that his relationship with Osimhen's entourage is "excellent", Napoli were threatened with legal action by the striker's agent last month after posting two bizarre videos appearing to mock the striker on the social media platform TikTok.
One of those clips showed Osimhen's penalty miss against Bologna in September with a high-pitched voice dubbed over the top, the same game where the Nigerian also exchanged words with head coach Rudi Garcia following his substitution.
Such incidents have plunged Osimhen's future in Naples into fresh doubt, but Napoli have insisted that rumours of a poor relationship are "entirely out of place", claiming that De Laurentiis's comments have been "distorted".
"SSC Napoli would like to clarify recent comments made by president Aurelio De Laurentiis regarding Victor Osimhen, given that his words have been distorted by certain media publications," Napoli said.
"President De Laurentiis did not say anything negative about Victor. He simply stated that after a series of lengthy contract negotiations which ended with the parties shaking hands and agreeing to continue together, Victor had second thoughts.
"President De Laurentiis hopes this is merely a pause for reflection. Over the coming weeks, when Victor will not be able to play as he recovers from injury, the president, Osimhen and his agent Roberto Calenda will sit down calmly to discuss the future. Describing relations between Osimhen and Napoli as frosty is entirely out of place."
Amid the off-field distractions, Osimhen has made a bright start to the new term with six goals from his opening eight Serie A matches, although the champions are languishing in fifth in the table.
Napoli's poor start has led to suggestions that Garcia is on borrowed time in the hotseat, and Julen Lopetegui is allegedly being lined up as a potential successor after Antonio Conte turned down the job.