The 21-year-old Portuguese is back at Anfield after spending last season out on loan in Spain with Granada, but looks set to spend another year earning vital first-team football.
Reds' boss Brendan Rodgers is thought to be keen on Ilori in the long-term, but for now is keen to further the youngster's education.
Bordeaux’s managing director Nicolas de Tavernost insists after showing the young defender around the club’s facilities, he is confident Ilori will return.
“I believe he has been convinced,” Tavernost told France Football.
“He visited the facilities and met the chairman, and we offered him a great show.
“I am confident.”