The Nigerian international has attracted interest from a number of teams over the past 18 months thanks to a succession of brilliant performances for the Italian giants, who are in contention to win the Scudetto.
Osimhen is sought after by a number of teams, including Manchester United, though it seems unlikely that they will succeed given his public pledge to the Neopolitans.
The 24-year-old said to TG5: "I play for a fantastic club, and my career is always progressing.
"I'm at one of the top clubs already, and I could not want for more. Forza Napoli, always.
Osimhen made his comments less than a month after admitting he aspires to play in the Premier League.
"I think playing in one of the top five leagues in the world (Serie A) is an amazing feeling for me," the player declared.
"While many people around the world view the Premier League as the best and strongest league, I currently play in the Italian Serie A, one of the best leagues in the world.
"I'm working incredibly hard to ensure that I one day realize my dream of competing in the Premier League.
However, like I previously stated, it's a process, so all I want to do is maintain my positive momentum.
Napoli is in position to win the Serie A championship for the first time in 33 years as they are 14 points ahead of Lazio in second place.
We are getting close to our goal, and Osimhen expressed his excitement about turning our dream into reality.
"The players always believed, and we always felt that we could accomplish something extraordinary, even when no one else did.
"The love from the city is remarkable; I've never experienced it. I'm eager to join them in their celebration at the stadium.
Tuesday night's second leg of their Champions League quarterfinal matchup against fellow Italians AC Milan will see Osihmen and his Napoli teammates back in action.
