The 21-year-old Italian, who moved to Anfield from Roma over the summer, has only recently returned to fitness following an injury-plagued first seven months at the club.
"I have to be honest, I've not had any contact with anyone at Fiorentina," Marco De Marchi told Firenze Viola.
"Fabio is happy at Liverpool because they are one of the most famous clubs in the world. He chose Liverpool in the summer and he's happy with his English adventure.
"If Fiorentina, a club who have shown they are ready to target youngsters with bright futures, are really interested then we'd thank them, but Fabio is just focused on getting back to full fitness after injury and thinking only of Liverpool."
Borini has scored one goal in 14 games for the Merseysiders this season.