The Spaniards are in the market for a left-back and Marca claim the Liverpool man is in their sights.
The Santiago Bernabeu outfit have the Brazilian as their first choice on the left of their back four, but with Fabio Coentrao out on loan at Monaco lack competition for the role.
With Marcelo struggling for fitness this term, right-back Danilo has filled in at times on the opposite flank, while the versatile Nacho is also able to feature there but lacks conviction.
Marca claim that Rafa Benitez’s men are considering a number of options, with Moreno the most likely to fit the bill.
The former Sevilla man was linked with the capital city side before he switched to Anfield and Madrid are said to be ready to rekindle their interest.
Moreno has shown at times that he can be a hard-working and exciting outlet on the left, but his defensive frailties have meant that the Kop have not been entirely convinced by him as yet.
The Spaniard lost his starting role in the side to Joe Gomez at the start of the season but has been reinstated since the young Englishman’s injury and improved noticeably under Jurgen Klopp.