Tare, a former striker who spent the bulk of his playing career at Lazio and joined Milan last summer alongside head coach Massimiliano Allegri, was speaking as part of DAZN's Giorgia's Secret series. He spoke at length about the differences between his two clubs, the challenge of building at one of European football's most demanding institutions, and what drew Modric to the Rossoneri.
"It's a pretty substantial change. With the name Milan, it's easier to convince players to join compared to when I was at Lazio, both for the history of the club and the financial capability."
Tare spoke of the personal significance of the appointment.
"The call from Milan? I was hoping for it. When it became a reality I think it was one of the most beautiful days of my life. I try to earn the right to be part of this club. To be part of this history you have to leave your mark."
On the subject of Modric, the 40-year-old Croatian midfielder who joined from Real Madrid last summer having grown up supporting the Rossoneri, Tare was effusive.
"I knew that as a child he was a Milan fan. When we met and talked about the project, I saw he had deep knowledge. He had other offers but he wanted to fulfil his dream of playing for Milan. His arrival in the team was very important, even at the level of mentality."
Tare indicated that a contract extension for Modric is already prepared, and that he expects the player to choose with his heart.
"He could choose with his heart. For me, he will stay at Milan."
Milan's season has fallen short of the Scudetto challenge Tare had hoped for, with Inter controlling the title race for the majority of the campaign. A succession of injury problems across the attacking line limited the club's consistency.
"We have important players. Unfortunately there are seasons with difficulties. For our strikers it was a complicated season from a physical point of view because many of them had physical problems that didn't allow them to find continuity."
He was unapologetic about where the bar must be set.
"Having the Scudetto in mind as an objective is our duty."
The full interview, which also touched on Rafael Leão's potential and Tare's own playing career, aired on DAZN on Friday.