Currently on loan with Bordeaux in Ligue 1, the 22-year-old Portuguese youth international has yet to make a senior appearance for the Reds, appearing just three times at Under-21 level since joining the club from Sporting in 2013.
He spent last season on loan with La Liga side Granada, making nine appearances - including a man-of-the-match performance in a 1-0 victory over Barcelona.
After returning to Anfield in the summer, Ilori was sent straight off to France, and has made 11 appearances for Bordeaux this term, scoring one goal.
His contract expires in the summer, and the Echo report claims that Sunderland have had scouts at recent Bordeaux fixtures to weigh up a potential move for the youngster.
Sporting director Lee Congerton has been lining up summer transfer targets for the Black Cats, despite not knowing who will be managing the first-team next season, and Ilori has been shortlisted to fill in the defensive positions with Wes Brown and Anthony Reveillere set to be out of contract come the close of this campaign.
It is unknown whether Ilori would be willing to transfer from Liverpool to Wearside, but with chances looking unlikely on Merseyside, the need for consistent first-team football could prove vital in the Black Cats securing his signature.