Napoli face German side Eintracht Frankfurt in the first leg of their Champions League round of 16 tie on Tuesday.
Luciano Spalletti's side have looked peerless in Serie A this season, sitting 15 points clear of nearest challengers Inter Milan after 23 matchdays.
Not since the days of Diego Maradona in 1990 have Napoli won the Serie A title.
Napoli also sailed through their Champions League group effortlessly, recording big wins against Liverpool and Ajax Amsterdam along the way.
Costacurta, who won five European Cups with AC Milan, believes Napoli can go all the way in Europe this term.
"I don't want this to pass as nonsense, but in terms of approach and attitude, Napoli are the strongest in Europe," he told Il Mattino.
"Obviously there are the others, and we know perfectly well that a competition like the Champions League is capable of drawing out of the players those motivations that maybe don't exist in the league. But I'm sure about one thing.
"At the moment, Napoli are stronger than Manchester City and all the others."
Costacurta added: "The strongest teams in Europe have not yet given great shows of strength in their leagues.
"That's why I'm convinced that right now Napoli have an attitude that legitimately allows them to be able to dream big."
