The Italian giants have been playing at a reduced capacity since renovating the Stadio Diego Armando Maradona in 2019.
After replacing metal fencing with glass, vibrational problems have caused the capacity to drop from 64,000 to 54,725.
The ground, previously known as the San Paolo, has been Napoli's home since opening in 1959.
Prior to the most recent renovation work, the stadium was also redeveloped ahead of hosting five matches at the 1990 World Cup.
However, after six years at a reduced capacity, owner Aurelio De Laurentiis is reportedly looking to expand.
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He is keen to increase support in order to boost the club's income from ticket sales as he looks at a way to fix the closed area.
De Laurentiis' dream is said to be a new stadium, though, which could be built if the issues at the Stadio Diego Armando Maradona cannot be fixed.
Both options already have the backing of the mayor of Naples, Gaetano Manfredi.
He even revealed in a recent interview that the plans are a 'priority' for him.
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Manfredi told Radio Kiss Kiss Napoli: "Changing the Maradona style was a priority for us. Today, it must be a shared choice with Napoli."
The mayor added: "There is no public funding, except for a small part.
"Calcio Napoli is considering the possibility of renovating the current stadium or building a new one.
"We are cooperating as much as possible because having a modern stadium in Naples is one of the priorities we have as an administration."
Plans are also in place for a new sports hall and improved public transport to be constructed in the area around the stadium.
Meanwhile, the space left by demolishing the Stadio Armando Maradona is expected to be used for a new arena.
Napoli are currently enjoying an impressive first season with Antonio Conte in charge.
The former Chelsea boss has his side second in Serie A, just a point behind Inter Milan with 11 matches remaining.
Scott McTominay scores and sends Napoli four clear in Serie A and went straight to Conte to celebrate