The Stadio Comunale Luigi Ferraris outfit saw Alberto Gilardino leave the club this week for Chinese champions Guangzhou Evergrande.
However, they have been quick to fill the striking void by bringing in the much-travelled Matri on a temporary basis.
Matri returned to Milan from Juventus in August last year before spending the latter half of the season on loan at Fiorentina.
However, Genoa confirmed on their website that Matri had arrived and passed his initial medical.
"Genoa announces that it has filed with the League offices documentation regarding the temporary acquisition of the sporting rights for Milan striker Alessandro Matri," read a statement on their official website.
"The player has completed visits certifying his fitness and is involved at this time in a series of tests relating to his return to competitive activity."
Genoa's president Enrico Preziosi spoke in the week of his pleasure at being able to replace Gilardino with Matri.
"We knew that Gilardino could leave, we have achieved a good operation in finding his replacement," he told Telenord.
