Sunderland are thought to be leading the chase for the Portuguese 22-year-old, and have had the centre-half watched on a number of occasions.
The Black Cats ran the rule over Ilori during the Under-21 clash between Portugal and Denmark last week but were joined by scouts from Celtic and Everton, according to the Shields Gazette.
Ilori signed for Liverpool in the summer of 2013, but has yet to make a first-team appearance since his £7 million move from Sporting Lisbon.
The Hampstead-born defender has impressed during loan spells with Granada and Bordeaux, and although Liverpool are reportedly monitoring his progress, Kolo Toure, Dejan Lovren, Mamadou Sakho, Martin Skrtel and Sebastian Coates are all thought to be ahead of him in the Anfield pecking order.
Initially a striker, Ilori converted to a defender during his time at Sporting Lisbon.
He also set the fastest time over 30 metre sprints while at Sporting’s academy, outpacing the likes of Cristiano Ronaldo, Nani and Ricardo Quaresma.
Celtic’s current first-choice centre half pairing of Virgil van Dijk and Jason Denayer faces being broken up during the close season, with Denayer set to return to parent club Manchester City and van Dijk a likely transfer target for a number of clubs.
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