Gilmour has been largely overshadowed by Scotland teammate Scott McTominay at Napoli this season.
But Galeone sees something special in the summer arrival from Brighton, telling Radio Kiss Kiss: "I liked Napoli against Empoli. If (Antonio) Conte's team manages not to concede a goal, then they score one and that's a big advantage.
"In Bologna I didn't like the defensive phase, then against Empoli they did it well and in fact the match came out.
"Gilmour is a player who knows how to defend and how to set up, together with (Stanislav) Lobotka, (Giovanni) Di Lorenzo and (Matteo) Politano he is good in that part of the pitch, as does (Andre-Franck) Anguissa.
"If the Cameroonian needs to rest, Conte has a good alternative. He doesn't look out of place in that role. If Napoli wants to strengthen for next year they must take at least one strong player for each role."