Ince, whose Blackpool contract has expired, is wanted by Crystal Palace after spending the back end of last season on loan at Selhurst Park.
However, the former Reds teenager has revealed that Inter have made an offer for him, and admitted that it would be a "dream come true" to follow in the footsteps of his father, Paul, who played for the Nerazzurri in the 1990s.
The Daily Star quotes Ince as saying: "Inter Milan is a serious option for me. There is an offer. To have a club of that stature showing that interest in me is a dream come true - especially with the history of my old man.
"It was 19 years ago this summer that he signed for them, and I can just about remember watching him play in the San Siro during the couple of years he was there.
"That they have come in for me now is quite amazing. Going abroad is definitely an option for me. You don't see many English players doing it - whether it is the risk of the language, I don't know.
"I have got to make sure I take some time to think and do what is right for me."
However, Wales Online has quoted Ince as saying that he would be keen on a move to Swansea City this summer.
"[Swansea is] a fantastic club which play fantastic football and Swansea has always been an interest for me ever since the transfer window has come about," said Ince.
“If Swansea are interested then definitely [it is an option]. It’s a fantastic club which is going places.”
Ince had been reportedly attracting the interest of his former club Liverpool last summer and in January, although the five-time European Cup winners were said to be put off by Blackpool's asking price.