The Dutch side is due to face Italy in the Nations League on Monday evening in Amsterdam.
They are operating under interim manager Dwight Lodeweges after coach Ronald Koeman left to take on the Barcelona job.
The favourite to lead Holland is Henk ten Cate, but Sky Sport Italia report that Allegri had been initially approached.
The former Juventus coach is currently out of contract, having taken a year out after he was fired by the Bianconeri at the end of the 2018-19 season.
Allegri won five consecutive Serie A titles at Juventus, and reached the Champions League Final twice.