The former Sporting Lisbon defender is London-born and could commit to England.
Ilori told liverpoolfc.com: "I used to watch Jamie Carragher play as a young boy and I would have loved to have had the chance to train and play with him. I'd also like to one day maybe fill his place, too.
"The last 24 hours have been chaotic. It's been nerve-wracking - I've just wanted to get things sorted out. But it's been exciting as well.
"I'm definitely looking forward to walking out there as a Liverpool player. Everyone talks about the atmosphere. I'll feel proud when I get the chance to walk out the tunnel at Anfield.
"It'll be a dream come true, especially at such a young age."
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