The club's sporting director, Daniele Prade, has revealed the club is looking at bringing in a natural goalscorer, though he believes signing either target could prove difficult.
Despite signing Giuseppe Rossi in the January transfer window, reports of interest in striker Stevan Jovetic has led the Viola looking at attacking alternatives.
Borini and Osvaldo played together for Roma before the former moved to Anfield in the summer, and even though Prade revealed the club's interest in the pair, he admitted it may be difficult to lure them away from their current teams.
"We are looking for a forward with the hunger for goals. A player who lives to score goals," he told Radio Toscana. "We like Fabio Borini, but it is unlikely that Liverpool will want to let him go. Osvaldo? I do not think that Roma will want to strengthen a direct rival of theirs, but you can never say never."
Vincenzo Montella's side is currently sixth in Serie A, 13 points behind leaders Juventus, and the club has scored the fourth-most goals in the league with 45 goals.