Los Blancos announced on August 24 that the Uruguay international had put pen to paper on a contract that includes a €1bn (£856m) release clause.
Valverde's previous deal had been due to run until June 2025, but according to Italian journalist Fabrizio Romano, Carlo Ancelotti's side wanted to add an additional two years to the contract.
Romano claims that Premier League clubs had approached Real Madrid to discuss the Uruguay international, and the La Liga giants wanted to ensure that there would not be any official moves for the midfielder during next summer's transfer window.
Valverde has made 105 appearances at club level and has been a vital player for Ancelotti's team at the start of the 2021-22 campaign, starting all three of their La Liga matches.
The 23-year-old represented Penarol before making the move to Real Madrid, initially turning out for their Castilla outfit, while he also spent the 2017-18 campaign on loan at Deportivo La Coruna.