Italian club have Champions League football this season and could afford to brush away bids for their star players, according to reports
Barcelona came in late for Italian striker Insigne, 26, who scored 21 goals for club and country last term.
Lorenzo Insigne celebrates scoring for Napoli against Nice in Champions League qualifying
Lorenzo Insigne is currently on international duty with the Italy squad
Meanwhile defender Koulibaly was wanted by City at the last minute as well, according to Football Italia.
City valued the Senegalese at roughly £60m but did not manage to land another defender on deadline day, with Jonny Evans also a target.
Pep Guardiola has made no secret of his desire to bolster City’s defence – and he managed to sign three defenders over the summer.
They brought in Kyle Walker from Tottenham, Danilo from Real Madrid and Benjamin Mendy from Monaco.
But that was after jettisoning Gael Clichy, Pablo Zabaleta, Bacary Sagna as well as keeper Joe Hart.
Barca, meanwhile, had been after another forward to bolster their ranks after the departure of Neymar and the arrival of Ousmane Dembele.
Kalidou Koulibaly was valued at about £60m by Manchester City
Kalidou Koulibaly goes up against Nice’s Mario Balotelli in Napoli’s Champions League qualifier
Ousmane Dembele signed for Barcelona for £110m
Frenchman Dembele, 20, joined the Catalan giants for a £110m – and they were prepared to fork out a similar sum for Insigne.
The Italian is at the peak of his powers, but question marks remain over his calibre at one of Europe’s elite clubs.
Insigne scored as Napoli all-but knocked out Nice during Champions League qualifying, as the Serie A side won the tie 4-0 overall.
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Diego Maradona and the Napoli Champions League squad stay at the same hotel