Ilori signed for Liverpool in the summer of 2013 for around £7 million from Sporting Lisbon, but his only game time has been on loan with other clubs - with Ligue 1 side Bordeaux his latest club.
The Sunderland Echo reported Sunderland's interest last week, but have claimed that both Everton and Celtic are interested in signing the defender.
If Ilori were to move on in the summer, Liverpool's original move to sign him would look increasingly odd, though they are monitoring his progress to see if he can make a contribution to the first team at Anfield next season - which could be likely if the Reds persist with a formation that requires three central defenders, and will perhaps allow Emre Can to undertake a midfield role from next season.
It will be interesting to see if Everton believe they can do some business with their biggest rivals and whether he would see a move to the SPL Champions as the right career move for him.
Realistically for Sunderland they will probably need to retain their Premier League status as they are currently embroiled in a relegation battle.
All four clubs had scouts had the latest Portugal under-21 game against Denmark, but seems that Ilori's situation is going to be watched closely leading up to, and during, the summer.