All three players impressed during the Under-21 European Championships in Israel this summer where Italy were beaten in the final by Spain.
"Verratti, Insigne and Florenzi will be part of our large squad in the future," he told La Gazzetta dello Sport.
"I like that there is competition. We still have a long way to go, even though we are on the right track.
"When there's change, the mechanisms won't always trigger quickly, but our philosophy has always remained the same."
Italy's senior team were beaten by Spain in the semi-finals of the Confederations Cup this summer.