The 23-year-old defender only joined the Reds in 2014, but has endured an up and down spell on Merseyside.
A number of error-strewn performances led to Brendan Rodgers dropping him in favour of teenage rookie Joe Gomez earlier this season, but he has since battled his way back to become a first-team mainstay under new manager Jurgen Klopp.
And it appears that his performances in recent months have alerted a former Liverpool boss in the shape of Rafa Benitez, who is eager to sign a left-sided full-back in January amid concerns about Marcelo’s niggling injury issues.
Moreno is seen as the sort of front-foot player Real need, and they are hopeful that a return to Spain may tempt the youngster – especially with EURO 2016 on the horizon.
However, Klopp is unlikely to let his man leave, especially as his only real back-up option is Jose Enrique, who hasn’t featured in first-team action for over 10 months.