The experienced Frenchman is set to add another year onto his deal through to the summer of 2023 – a reward for the player’s fine form in recent years.
Whilst there is not yet a firm agreement between the two parties, it is said there is a firm understanding between the two and a new contract is imminent.
It is standard in Real Madrid news for players aged over 30 to sign only one-year contract extensions when their existing deal expires.
The Frenchman has netted 10 goals in his last 10 games and has 25 strikes in 36 outings this campaign – including 19 in La Liga from just 26 outings.
Benzema has been in red-hot form since Cristiano Ronaldo left the Spanish club three years ago – scoring 82 goals in less than three full campaigns.