Milan have completed the signing of Anastasio, with the 2008-born attacking midfielder set to begin his time at the club in Serie D with the Milan Futuro project, while the club is also pushing hard on a separate front to sign Zaniolo.
Announcing the Anastasio deal, Milan said in an official statement: "AC Milan is pleased to announce it has signed the player Max Vincenzo Anastasio, who will be part of the Milan Futuro project, dedicated to the growth and development of young talent. The midfielder, born in 2008, played for Bologna FC and has now chosen to join the rossoneri colours."
On a separate and considerably higher-profile front, Milan have moved into pole position to sign Zaniolo from Udinese, with the club meeting the striker's agent, Claudio Vigorelli, on Tuesday evening to discuss the terms needed to complete a deal.
Zaniolo, who did not report for Udinese's pre-season training as his contract standoff with the club drags on, could be used as an attacking midfielder in Ruben Amorim's 3-4-2-1 system if a move goes through.
The relationship between Zaniolo and Udinese has grown increasingly tense, with talks over a new contract still deadlocked. Udinese have offered €1.5m net per season, while the player is understood to be holding out for between €400,000 and €500,000 more to reflect his performances last season.
With no agreement in sight, a sale is not being ruled out, and Milan are reported to be ahead of both Juventus and Bologna, who are also monitoring the situation, in the race to sign him.
Milan's dual approach captures the club's summer strategy under Amorim: investing in academy-age prospects like Anastasio for the long term, while simultaneously working to bring in a proven Serie A performer who could add immediate quality further up the pitch.
Anastasio arrives after progressing through Bologna's youth ranks and represents the kind of low-cost, high-potential addition Milan have prioritised as they look to rebuild depth across their academy sides.
Zaniolo, by contrast, would represent a much more significant statement of intent, giving Amorim a versatile attacking option with Serie A pedigree and recent European experience, should the deal be completed before the market closes.