The Spaniard has managed to compete only 90 minutes on one occasion so far this season. However, the Reds are very interested in landing the highly-rated 22-year-old striker next month.
Liverpool manager Jurgen Klopp is thought to be keeping an eye on the player’s situation and could make a surprise move in the January transfer window.
Klopp is determined to reinforcements to Anfield this new year, with the Merseyside outfit desperate to get their push for the EPL title back on track.
Rodriguez, who has fallen down the pecking order at the Bernabeu, is also thought to be a target for Arsenal, Inter Milan and Napoli.