Nicola's job is reportedly under threat after Sunday's 3-0 Serie A defeat at Chievo marked the Tuscan outfit's third straight loss and their eighth of the campaign.
The team have won just once in their last 11 matches, but a club statement read: "Regarding reports in the Italian press of an eventual coaching change at Livorno, club president Aldo Spinelli wants to clarify that the Amaranto club has never contacted, nor thought of contacting, other coaches.
"Our group has been created following the project indicated by our coach Nicola and, up to Sunday's game against Chievo, the team has produced good performances."
Nicola guided Livorno to promotion to Italy's top flight last summer in his first season in charge.
Livorno are 18th in the standings, level on 12 points with Bologna, who hold the last position of safety.
The Amaranto host AC Milan on Saturday.