Galtier is the latest coach to be linked with the Newcastle hot seat that is set to be vacated by Crystal Palace-bound boss Alan Pardew in the coming days.
Caiazzo moved quickly to dismiss those rumours, claiming they are "insulting" to the Ligue 1 outfit, who are challenging for domestic honours after finishing fourth in 2013-14.
"Do you really think that Galtier, in the middle of a season in which he is aiming for a top three place, would leave like a thief for a club like Newcastle?" Caiazzo told Eurosport.
"It would be insulting to suggest that Christophe is even slightly interested in such a rumour.
"Christophe is not a man of money. He has been here for years and is fully engaged in the project."
It is not the first time Galtier and Newcastle have been linked, with the Premier League side reportedly approaching the 48-year-old in May.
