Cristante's form this term has sparked transfer speculation involving both United and Juve.
And Lippi, discussing the young midfielder's progress, revealed his father Marcello Lippi, now China coach, was a big fan of Cristante when he was coming through at AC Milan.
Lippi told Tribalfootball.com: "In the past days my Dad spoke well about him. He is a good player, he surprised me and I am pleased to admit it.
"He always showed his qualities, when he was playing in youth soccer, even if at the times he never amazed me.
"(Gian Piero) Gasperini changed him a lot, now Cristante is a different player, a totally different one. In the past years he used to play as a defensive midfielder, now he plays as a box to box midfielder. I congratulate the player and Gasperini for his growth. The manager is a master."
However, Lippi warns Cristante about quitting Atalanta too soon.
"At the same time, anyway, I think it would be best to take it easy on him. I'd like to see him play at this level with continuity at Atalanta, at least for a couple of years. Of course he has great qualities, but we need to see him play with continuity.
"I think he can become a top player, good for a top team, even stronger than Italy's top teams, but he's having his first truly great season. Time is on his side, there's no need to rush."
The agent says Cristante is the ideal example of why Serie A clubs needs to back the nation's young players in greater numbers.
Lippi concludes: "Italian teams have to make youngsters play earlier, but we need more time to judge a player. Many young players in the last years passed to bigger teams, but the risk is to pay them too much."