The London-born 20-year-old has represented Portugal at youth level but is yet to win a senior cap and the Football Association has opened the door for the defender to represent England.
Ilori, who moved to Anfield on deadline day in a £7million switch from Sporting Lisbon, is open-minded about his international future.
He said in The Sun: "I think I would like to stay loyal to Portugal.
"I lived around Kentish Town and was eight when we moved to Portugal.
"My mum is Portuguese and my dad was born in London.
"I'd never close a door but if I have a choice, it's not a bad one to have."