The England Under-21 international winger is out of contract this summer after his deal with Blackpool expired.
The 22-year-old arrived in Milan on Sunday night with his father Paul - who played for Inter during the 1990s - to meet club officials and discuss a possible move to the Nerazzurri.
The Blackpool player spent the second half of last season on loan at Crystal Palace and has attracted interest from a number of leading clubs.
"I'm not an Inter player yet," Tom Ince said to Sky Italia. "I'm very happy to be here two or three days in the meantime.
"Inter is a fantastic squad and Italy is a great country, where I have many fond memories.
"I remember the San Siro with affection, players like (Javier) Zanetti, (Massimo) Paganin and (Aron) Winter.
"We lived in Como.
"I'm young, English, a winger, a fun player to watch," he said. "Inter are changing, they have new young players and a new owner.
"(Inter president Erick) Thohir has told me that there are changes taking place, that he wants to return Inter to being big, to win in Italy and in Europe, to take them back to the level of great clubs on and off the pitch.
"This is fantastic for me."
Paul Ince is excited by the possibility of seeing his son wear the Inter jersey.
"This is an incredible story," he said. "It's incredible Tom is here at 22, he was five back then.
"I spent a beautiful time here.
"For me Inter is love, the fans transmit passion.
"The important thing for Tom is to be here today, to see the training ground, get to know the stadium and the city.
"Then we will go back home and take a decision.
"I'm here now for my son, I think we will know more in a couple of weeks."
Inter Milan's technical director Piero Ausilio also confirmed earlier this month that his club were among those looking to land Ince.