De Zerbi was appointed as manager of Brighton after they saw Graham Potter leave for Chelsea, with his last job being with the Ukrainian club.
Juventus coach Massimiliano Allegri has been under the spotlight due to the Turin club making an indifferent start to the season, and he could be a casualty as the campaign progresses.
Nicolini revealed he offered De Zerbi to Juventus before Brighton came to the fore with an impressive project and managed to appoint the Italian manager.
The Shakhtar Donetsk sporting director thinks that the Italian giants missed out on a great prospect by not appointing De Zerbi, who he believes would have been an ideal fit at the club.
Nicolini, asked if any Italian sides enquired about De Zerbi, was quoted as saying by Italian outlet TuttoJuve.com: “There were no official requests.
“I also offered De Zerbi to Juve, but then Brighton came forward with an important project.
“The Bianconeri have lost a great opportunity.
“It would have been the right time to sign him.”
De Zerbi has extensive experience in Serie A, but he now comes to the Premier League in the form of Brighton and the Seagulls supporters will be hoping he can hit the ground running.