The Daily Mail says Dortmund have asked to take the 21-year-old Ilori on loan.
The Portugal U21 international would move to BVB as a replacement for Manchester United target Mats Hummels.
Ilori, bought for £7million by Brendan Rodgers from Sporting Lisbon last summer, was sent out on loan to Granada last season.
However, he impressed scouts in Spain and Germany, with Dortmund expressing an interest. Dortmund had already eyed up Ilori while he was at Lisbon, but were reluctant to splash the cash on the youngster in 2013.
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