The 53-year-old Italian takes charge of the Old Lady for a second time, after the sacking of Andrea Pirlo last month.
According to Goal, Allegri and Juve chiefs have already held a meeting to discuss their plans for the upcoming transfer market and Ronaldo's future was at the top of their priority list.
The Portuguese star has been heavily linked with a move away from Juventus this summer, despite the club securing Champions League qualification for next season, with former club Manchester United believed to be interested in his services.
Juve are understood to be open to the departure of the 36-year-old, who is entering the final year of his contract, but only if the right offer is made.
Allegri is keen for Ronaldo's situation to be resolved quickly one way or another, and wants clarity on which positions he is to target this summer.