The Italy international was on the books of Milan at the start of his career, but he failed to make an impact at the San Siro.
He has been linked with a return to Milan after Juve bolstered their attacking options by signing Carlos Tevez and Fernando Llorente earlier this summer.
However, Marotta told Sky Italia: "Matri is currently our player. Milan have never asked us about him."
Marotta, though, accepts that, with six strikers currently in Antonio Conte's squad, someone may be shipped out before the transfer window closes, with Matri also having been linked with Everton, Newcastle, Sunderland and Napoli.
He added: "This group can give coach Conte the possibility of technical flexibility. Each one can have a different role. We are okay in this way.
"Clearly, having six strikers, there is not space for all of them. If someone should ask us to go elsewhere we would be sorry, but we will do what we do."
Meanwhile, speaking after Milan started the new Serie A season with a surprise 2-1 defeat at promoted Verona, Rossoneri coach Massimiliano Allegri was not thinking about new signings.
Allegri, whose side face PSV Eindhoven in the second leg of a UEFA Champions League qualifier on Wednesday, said: "In this moment, this is the group at my disposal.
"Let's think about the Champions League match against PSV Eindhoven on Wednesday and then we will see."