Benzema has been brilliant since Zidane was reappointed as Real manager back in March, netting eight goals and providing three assists in the eight La Liga games since his compatriot's return.
The 31-year-old has now explained the relationship he has with Zidane and said he only wants to improve on the pitch, per Le Quotidien (h/t AS via Football Espana):
"It’s very strong. It's a relationship that started a long time ago, I met him before he was a coach and he helped me a lot. We talk about football and life, he is like my big brother and he has helped me a lot. It's more than friendship, it's like he is part of my family, but that does not stop him from reproaching me or the other way round.
"My time at Real Madrid since 2009 has been incredible, as time goes by, it seems very strange to me. I am proud of the way my time here has progressed. It is not bad for a footballer's career, especially being in one of the best clubs in the world. I feel good in this club. This season has been complicated because we have not achieved titles, but personally for me it was good and I want to continue this improvement."
Benzema's form has been one of few silver linings for Real in a 2018-19 season that has been largely disastrous.
The departure of Cristiano Ronaldo has had a major impact on Real's goalscoring, and they look set to finish the La Liga season with their worst return since 1999-2000, when they scored only 58.
Benzema's tally of 21 goals this term in the Spanish top flight puts him 13 ahead of Gareth Bale, Real's second top scorer in the league with eight.
Ronaldo averaged just under 35 goals a season in La Liga for the nine campaigns he was at the club, and it is clear Real need to strengthen their attack next term in order to become title challengers once again.
That could theoretically put Benzema's place in the side under threat, but his form in 2018-19 and good relationship with Zidane means he will surely remain a key first-team player next term.
Eden Hazard is also looking like a potential new recruit in the front line:
Given he prefers to play on the left-hand side of the front line, Benzema's No. 9 spot would not be affected by his arrival. And the pair could likely flourish together.
Hazard has netted 16 goals and provided 15 assists in the Premier League this term, the kind of return Real could really benefit from alongside Benzema's contribution.