Ilori has represented Portugal at various youth levels but he was born in London and could still switch allegiance having not been capped at senior level.
The 20-year-old joined Liverpool from Sporting Lisbon in a £7million deal on transfer deadline day last week.
Ilori told the Liverpool Echo: "I think I would like to stay loyal to Portugal as I've played in every age group for them.
"But I would never close any doors and there is no decision to make yet. If I have the choice then it is not a bad choice to have.
"I lived in a few places around Kentish Town. I was eight when we moved to Portugal. My mum is Portuguese. I didn't play in any football league when I was in London but just played with my friends.
"My English family are originally from Manchester and they all moved to London. My dad was born in London as well."
- Sports & Recreation