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.
|14/1||Liverpool are 14/1 with William Hill to win the Premier League|
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."