The Costa Rican, who only moved to Madrid in the summer, is said to be unsettled and contemplating his future at the Bernabeu.
The stopper has only made six apperances this season and according to his agent, has told Madrid he would like to leave.
These comments have since alerted a number of top clubs across Europe, Liverpool being one.
Rodgers is said to be a big admirer of Navas and is preparing to step up the interest in the summer.
The signing of Navas may well see the end of Mignolet’s career at Liverpool, the Belgian so far having a turbulent season, making several costly mistakes.
By Connor Billington