Both clubs are working towards finalising a deal which would see the Danish prospect move to the Diego Maradona Stadium on an initial loan with a buy option worth €30 million.
Lindstrom is expected to travel to Italy for his medical tests soon once the paperwork is sorted out.
The Dane has been viewed as a replacement for Hirving Lozano, who has been linked with an exit throughout the summer.
The Paretnoepei are pushing to offload the Mexican international, who has been deemed surplus to requirements. His contract expires next summer.
Former club PSV Eindhoven have made a late approach, submitting an offer worth €15 million, including bonuses.
Lindstrom has also been on the wishlist of fellow Serie A rivals AC Milan and Juventus, but the Partenopei have won the race for his signature.
Being one of the most talented prospects of the Bundesliga, the 23-year-old has been a key figure for Frankfurt, playing a big part in the 2021/22 Europa League triumph.
With the ability to play in multiple positions from attack to midfield, Lindstrom has accumulated 14 goals and assists apiece for Frankfurt in all competitions.
The Neapolitans recently suffered a setback after losing out on top midfield target Gabri Veiga, and it remains to be seen whether they will sign an alternative before the end of the transfer window.
Napoli are keeping tabs on Genoa’s Albert Gudmundsson as a potential attacking target.
Rudi Garcia’s side have made an impressive start to the season, winning back-to-back games in Serie A.
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