Friday afternoon saw the San Siro outfit announce the departure of influential midfielder Boateng - who made exactly 100 appearances in all competitions for Milan - to Schalke while 29-year-old striker Matri left Juventus to rejoin the club he left in 2007.
The visit of Cagliari to Milan may briefly distract Galliani from his double pursuit of CSKA Moscow midfielder Keisuke Honda and Real Madrid playmaker Kaka - a Champions League winner with the Rossoneri in 2007.
He told acmilan.com: "Our transfers dealings depended totally on us gaining access to the group stage of the Champions League, so now we've been able to do a few deals.
"Who knows, something else may still happen.
"Matri is back. The number nine shirt goes to Matri, as back in my day the centre-forward always wore nine.
"His arrival reminds me of when Pippo Inzaghi came here 12 years ago, he was around the same age as Matri is now.
"Boateng was a lightning-quick operation which was all done in a day and a half, with the approval of everybody involved: Schalke, ourselves and the player.
"Kaka will be very hard to get and I think we're more likely to get Honda than him. I reckon it will be one, not the other."
Milan are still missing striker Giampaolo Pazzini while Riccardo Saponara, Luca Antonini and Daniele Bonera remain on the treatment table.
Unlike the Rossoneri, whose season began with a shock 2-1 defeat to newly-promoted Hellas Verona, Cagliari got off to a winning start by beating Atalanta by the same scoreline in Trieste.
The Sardinians, who have finally been given permission to return to their former Stadio Sant'Elia home, do not expect to conduct any more transfer business before the window closes on September 2.
Rossoblu president Massimo Cellino told his club's official website: "In relation to reports that have appeared in certain media outlets about transfers involving Rossoblu players, the market is closed for both incoming and outgoing players."
Winger Andrea Cossu and full-back Francesco Pisano will not feature at San Siro due to injury while striker Marco Sau has identified Mario Balotelli as the biggest threat for the hosts.
He said: "Balotelli is obviously the number one danger, but we should be scared of all the Milan players. We're talking about a really strong team that can hurt you at any given moment."