The Frenchman has overseen a trophy-laden tenure with Los Blancos since his appointment in 2016, including two Champions League trophies and a La Liga title.
However, Real have struggled this season and currently sit fourth in the league, 16 points behind rivals Barcelona.
Despite admitting to penning a new contract with the club, Zidane emphasised that he "cannot look two or three years ahead because having the contract does not mean anything".
According to the Daily Star, the Madrid hierarchy have not been impressed with Zidane's work this season and will be seeking to bring Low to the Bernabeu dugout in the summer.
Tottenham Hotspur manager Mauricio Pochettino has also been linked with the Merengues post.