The experienced Brazil full-back won Serie A and the Coppa Italia, as well as reaching the Champions League final, in his first season at Juve since completing a free transfer from Barcelona last year.
The 34-year-old, who is under contract until the end of June 2018, has been linked this week with Manchester City, who are coached by Pep Guardiola, his former boss at Camp Nou.
Juve team-mate Gonzalo Higuain posted and then quickly deleted a video on Twitter in which he appeared to be saying goodbye to his team-mate.
But Alves appears to be unimpressed by the rumours, angrily responding to one Italian media company's speculative tweet.
He wrote: "Don't spread s***, pipa [Higuain] sent a video for me in a television programme. Don't do your job badly, please."