Wigan have announced Uwe Rosler as their new manager after agreeing compensation with Brentford.
Marseille have parted company with manager Elie Baup in the wake of Friday's defeat to Nantes at the Stade Velodrome.
Borini, who joined Liverpool last summer, has endured a frustrating first season at Anfield with a series of injuries restricting his first-team chances.
The forward's agent, Marco de Marchi, insists he has not had any contact with Fiorentina and that Borini remains committed to Liverpool.
"I've heard the Fiorentina rumours, but there has been no direct contact," said De Marchi.
"Fiorentina are a club on the launch pad, they have laid the groundwork for an important project by signing great players and results will soon arrive.
"However, Borini has bought into the Liverpool project and they are one of the most important clubs in the world and he wants to be back by the end of the season to play in the European Under 21 Championship with Italy."