Biabiany came close to joining AC Milan last week.
"We are very proud that Biabiany has wanted to stay," Leonardi told Parma's official website.
"It means that there is a valid project at the club. We will strengthen his will to remain by giving continuity to the contract that binds us.
"By the way, it is absolutely not true that we went out to offer our players, because we have very good kids that we value very much."