The 20-year-old center back, 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 center back joined the Reds for 7 million pounds from Sporting Lisbon last summer but has not featured for Brendan Rodgers' side this season.
The 20-year-old has played for Liverpool's under-21 side and been named on the first-team bench on three occasions but has yet to be trusted in the Premier League, despite a raft of defensive injuries suffered by the likes of Daniel Agger and Kolo Toure.
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 senior side.
Granada sits 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."