Real Madrid are considering making signings in the January transfer window and the club continues to retain interest in Liverpool right-back Trent Alexander-Arnold as their preferred option to address their defensive issues, sources told ESPN.

However, sources told ESPN there is an understanding at the club that agreeing a deal with Liverpool in January would be difficult and they are exploring other options as well.

A source told ESPN that reinforcing the defence is considered a priority after successive defeats at the Bernabéu to Barcelona and AC Milan.

Alexander-Arnold emerged as Madrid's top candidate following a season-ending injury to Dani Carvajal last month. However, it was unclear whether Madrid would wait until the summer to sign the full-back as a free agent when his Liverpool contract expires or would try to sign him in the winter transfer window.

But Lucas Vázquez's struggles at right-back in the defeats to Barcelona and Milan have sped up Madrid's pursuit of the England international and a source told ESPN they are keen to address their defensive problems in January.

While Ancelotti has publicly maintained that Madrid aren't expecting any reinforcements, sources told ESPN that the Italian and his coaching staff believe they were short on players after the departure of Nacho Fernandez in the summer and are eager to make additions to the squad.

David Alaba has been injured for almost a year and sources told ESPN that there is pessimism about his recovery as the timetable has been repeatedly extended and his cartilage problem continues to persist.

With Jesús Vallejo out of Ancelotti's plans, Éder Militão and Antonio Rüdiger are the only centre-backs available to the Italian. Aurélien Tchouaméni, who was often fielded at centre-back, has been ruled out for a month after spraining his ankle against Milan, a source told ESPN.