Keane was a mainstay in the United side from 1993 to 2005, winning seven Premier League titles in an incredibly successful stay at Old Trafford.
However, the Irishman has admitted before that he considered leaving the Red Devils at times during his 12 year spell at the club, and Lippi has revealed that Juve nearly got their man.
I loved (Roy) Keane, Lippi told the Daily Mail. 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.
(Ole Gunnar) Solskjaer was very good as a player and I hope he will do very well as a coach: he deserves it.
Lippis two spells in charge of Juventus ran from 1994-99 and 2001-04 and it is not clear at what point Keane was nearing a move to Turin.
The 48-year-old has previously said he spoke to Juventus about a possible switch, along with another giant of European football, Bayern Munich.
I wouldnt say I had regrets about not going abroad but I think it would have been a nice experience to play for a different team, Keane told ITV.
When my contract ran down on a couple of occasions, I spoke to a couple of clubs, Bayern Munich, Juventus. And yeah I was very tempted I have to say, but there was a bit of fear.
Contracts were agreed but I just never felt strong in wanting to go for it because I was very happy at United.