Palombo has been linked with a move away after relegation, but sporting director Pasquale Sensibile insists the player is going nowhere.
"He won't be leaving Genoa," said the official. "We've had some reassuring signs from the player so there is no problem.
"Palombo will stay here and he will continue to be our captain.
"I can imagine that Napoli have spoken to the player, but he prefers to stay with us. Palombo has shown great attachment to the city and the shirt."