The Rossoneri vice-president confirmed he was keen on bringing the former Santos striker to Italy this summer
The 21-year-old sealed his long-awaited move to the Camp Nou on Monday after a protracted transfer saga, with Barca vice-president Josep Bartomeu confirming the club had spent more than originally planned on the Brazilian as a result of interest from other clubs.
And while Real Madrid also had a bid accepted for the now former Santos man, Galliani has admitted the Rossoneri were keen on bringing the Brazil international to San Siro, only for financial restraints to bring an end to their interest.
"Neymar? We tracked him, which is something that nobody knew," he told reporters.
"We could not make it happen. He was just too expensive. They [Barcelona] have double the budget we have. No Italian team could have afforded him."
Milan have a long history of purchasing Brazilian talent, with the likes of Cafu, Ronaldo, Ronaldinho, Robinho and Thiago Silva all pulling on the red and black shirt in recent times.