The 22-year old has been on loan at Crystal Palace since January, and, with the wingers contract expiring at the end of the season, Internazionale can poach him for as little as £155,000 in compensation.
The Daily Mail reports that, as well as Inter, Olympiacos, Everton and Tottenham Hotspur are tracking the English under-21 international, although the compensation fee required by clubs based in England would be higher.
Ince is the son of former England captain and Blackpool manager Paul Ince, who played for Inter between 1995 and 1997, and the youngster could take inspiration in following his fathers footsteps - especially after a less than productive spell in the Premier League.
The senior Ince spent two successful seasons with the Nerazzurri, helping them to the 1997 UEFA Cup Final, although, when offered a new, improved contract by Massimo Moratti, Ince decided to return to England - signing for Liverpool, the club where Tom started his career.
A grand total of seven appearances for the Eagles - with only four starts - has not been the career defining move intended, although current boss Tony Pulis is still determined to sign Ince permanently in the summer, having confirmed their survival in the Premier League.
Pulis expressed his admiration of Ince to The Guardian, whilst also admitting that securing his signature will be a priority following the close of the season.
"He's one that we'll look at once things are done.
"I'd love to sit down and get something done with him because I think he's a top player. Tom has been absolutely fantastic. Tom Ince will be a top Premier League player, without a shadow of a doubt. He's got all the attributes and everything else."
It has been a rather disappointing season for Ince, with a rumoured call-up to the England World Cup squad dissolving as Premier League appearances became hard to come by.
Whether Ince commits his future to the London club will have to be seen, although the lure of playing in a new league - in a new country - at a club where his father once spent two seasons may be a draw too strong to refuse.