Montolivo is continually being linked with a move away from the Viola following his refusal to extend his expiring contract, and clubs such as AC Milan and Juventus are reportedly monitoring his situation closely.
Nevertheless, Branchini has made it clear that a winter transfer is not an option at present.
"At the moment, there is nothing happening. There are no options. The interest of AC Milan? That's more speculation in the press than it is a realistic option," Branchini said to Sky Sport Italia.
"Fiorentina have declared him unsellable, so I really don't think he will leave in January. Riccardo also has the intention to stay until June and that has to be respected."
The 26-year-old midfielder has made over 200 competitive appearances for Fiorentina since joining them from Atalanta in the summer of 2005.
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