Keane, 48, was a dominant midfielder during his time at Manchester United and put in the performance of his career in the 3-2 away in Turin en-route to their memorable Treble-winning campaign in 1999.
However, a deal fell through because personal terms were not agreed.
In an interview with the Mail, ex-Juve coach Marcello Lippi said: "I loved (Roy) Keane.
"He was very close to moving to Juventus but then failed to negotiate. I also loved (Paul) Scholes: he would have liked it anywhere and always played."