The highly-rated winger ended the 2013/14 on loan at Crystal Palace, having made the step up into the Premier League from Blackpool.
Several top flight clubs expressed an interest in his services in January, but it was Tony Pulis who landed the England U21 international.
Palace are believed to be keen on reaching a permanent agreement, while Blackpool have tabled fresh terms, but Ince will again be keeping his options open ahead of another transfer window.
That has allowed Inter to join the chase, and they are hoping to make the 22-year-old the second member of his family to join the ranks at the San Siro - following in the footsteps of his father, Paul.
Ausilio has, however, been quick to point out that a deal is far from done and that Inter face fierce competition for Ince's signature.
He told reporters on Saturday: "He's a young player with an expiring contract who is weighing up several offers.
"It's definitely not a done deal for Ince. It's an intriguing possibility, him coming here in his father's footsteps."