The 20-year-old central defender, who joined the Reds on deadline day last summer from Sporting Lisbon, has moved to the Liga outfit in search of first-team football
The Portuguese centre-back joined the Reds for £7 million from Sporting Lisbon last summer but has not featured for Brendan Rodgers' side this term.
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Ilori, who was born in London, has featured for every Portugal youth team up to the Under-21s but is still waiting on his maiden appearance for Paulo Bento's side.
Granada sit 10th in Spain's top flight and drew 0-0 with Osasuna on Saturday.
Despite not yet breaking into the Liverpool first team, Rodgers said earlier this month that Ilori has a bright future at Anfield.
"I wanted to try to protect the present and the future of the club [by signing Ilori]," he said. "He is one for the future, but he can be a really big talent."