Ilori, who was born in London, signed for Liverpool on transfer deadline day from Sporting Lisbon for a reported fee of £7million.
The 20-year-old is eligible to represent both nations and has played for Portugal at several age groups, up to Under-20 level.
And while Ilori refused to rule out playing for England, he has said he would prefer to continue his career with Portugal.
Ilori told TheLiverpool Echo: "I think I would stay loyal to Portugal for them at every age group.
"I was eight when I moved to Portugal and my mother is Portuguese. My English family are all from Manchester and my Dad was born in London as well.
"But I would never close any doors and there are no decisions to make yet. If I have a choice then it is not a bad one to have."
Ilori, who scored once in 11 Primeira Liga games for Sporting last term, could make his Liverpool debut when Brendan Rodgers' side travel to Swansea City on Monday.
