The former Blackpool star was wanted by the Serie A giants in the close season, and the winger flew out to Italy to discuss terms on a move to San Siro.
However, with Ince also attracting attention from a number of Premier League clubs, the son of former Nerazzurri star Paul, opted to sign for the FA Cup runners-up.
Despite Inter's struggles in Serie A last season, the snub raised eyebrows throughout football, but Ince has said that his decision was reached after factoring in a number of issues.
The Mirror quotes Ince as saying: “It was very close. I went out there and had a good three or four days [in Milan]. We went to the San Siro, the training ground and it was unbelievable to stand there in that environment. That’s an ambition of mine, but I don’t think you should jump the gun.
“You’ve got to realise that when you’re a young lad you have to educate yourself and make moves for the right reasons. That’s all that matters.
“At my age I have to think about football development. I’ve come here to be educated. Anyone can go to a status club and pick up five or six times more money than you could do in the UK, but I’m a footballing person. That’s why this move is right.
“There are not many people who have [voluntarily left Liverpool] - taken a step back and gone a different route. I’ve gained strength and experience from playing every week. Now I feel it’s the right step to play in the Premier League and I can’t wait to get started.”
Ince has been one of three big signings for the Tigers this summer, and Steve Bruce has splashed out around £15 million already on Jake Livermore and Robert Snodgrass.