The World Cup winner's contract with the Rossoneri is just about to expire and his representative has floated the idea of his client joining Andrea Pirlo in Turin
The former Italy international is a free agent, having failed to agree a new deal with AC Milan, and has been linked with both Rangers and Lazio over the past week.
However, there has also been talk that Juventus could be about to offer veteran midfielder the opportunity to join former Rossoneri team-mate Andrea Pirlo in Turin.
"I haven’t spoken to them yet, but I can guarantee anyone who signs Gattuso will be getting a bargain," the player's representative, Andrea D'Amico, told Tuttosport.
"He has got himself back in exceptional physical condition and in my 23-year career I have never known a player with the determination and character that Gennaro is able to bring to a group."
Sebastian Giovinco, who Juve co-own with Parma, has also been linked with a return to Turin in recent weeks but D'Amico hinted that the attacker will only go where he is guaranteed regular football.
"Parma gave him the keys to the attack and he has repaid them by scoring many goals because he was able to release his talent," he pointed out.
"I will advise him to go where he will be considered the great player that he is. Sometimes, unfortunately, Italians must pay the price for not having a foreign name!"
D'Amico also argued that Juve should also be looking another two of his clients, goalkeeper Andrea Consigli and centre-half Salvatore Bocchetti.
"If they are looking for an heir to [Gianluigi] Buffon, they could consider Consigli, who is doing very well at Atalanta," he reasoned.
"Bocchetti is a very mature guy for his age . He will be out of contract in 2013 and two years ago [Rubin Kazan] paid €10 million [for him]."
Juventus coach Antonio Conte admitted after signing a new deal with the club earlier this week that he is keen to strengthen his Scudetto-winning squad this summer.