The forward has been linked with a switch to Tottenham Hotspur this summer, but Internacional's director of football Luis Cesar Souto de Moura revealed that an offer had been turned down from the Italians.
"We received an €18m verbal offer from Napoli, according to the player's agent," de Moura told Lancenet.
"We don't accept that this is Leandro Damiao's value. We are certain he will play the 2014 World Cup with Brazil's national team.
"We have not had any talks about setting a value as we don't intend to sell the player. The offer that was presented to us was lower than what he is worth."
Damiao missed out on Brazil's Confederations Cup win after suffering an injury shortly before the competition got underway.