The Uruguayan striker remains a strong target for City as well as Chelsea and Real Madrid but De Laurentiis said the former is the only club to have made official contact, however, the offer was too low.
"The only meeting I've had has been with Manchester City, but the offer was inadequate," he told reporters.
He added: "If a club offers 63 million euros (£53.3m) then we would allow him to leave. The release clause will have been activated.
"It's not fair that Cavani has distractions while he is playing in an important tournament like the Confederations Cup.
"Should we receive an offer, then fine. If this offer doesn't arrive the Cavani will stay in Italy with us."