Napoli did not get Conte for several reasons and may also be influenced by the financial level of the club. Conte has been linked with Napoli but without smooth negotiations it will force them to look for other options.
Gasperini is considered a suitable option because he has a good track record at Atalanta which succeeded in winning trophies and if you look further, what Gasperini achieved was not that impressive in previous seasons.
Napoli must improve if they want to compete next season and they must determine a suitable coach in an effort to create solidarity within the team. If not, a season like this will happen again because they don't have a coach who is able to provide a winning share in every match.
Seeing Napoli's desire to bring in Conte as Napoli's coach next season, it feels like it will fail, because we know that the arrival of Conte, Napoli's manager, is required to buy several players who are technically good according to the coach's game, but it feels very difficult for Napoli because of financial problems, they don't really good, if they release some of their players maybe this will happen to Napoli who want to control Conte.
Gasperin is a very good coach this season with Atalanta, of course he is one of the right candidates for Napoli but it is very difficult for Napoli who want to recruit to the Club, because of his success with Atalanta this season they will play in the Champions match which is certainly a good opportunity to bring his and Atalanta's name to a better level, and if we see that Atalanta is better than Napoli at the moment, of course Gasperin will not leave Atalanta and vice versa with what Gasperin has given to Atalanta, Atalanta's management does not want to part with him.
I think Ole Gunnar Solskjaer is quite suitable to handle the Napoli team, Ole is a former Manchester United coach and is very skilled at rebuilding Napoli's reputation which is currently in decline.