The Uruguayan has become a prominent member of Carlo Ancelotti's side's midfield, making 20 appearances, scoring eight goals, and contributing four assists.
Valverde, 24, is quickly becoming one of Europe's most renowned talents, and his compatriot Luis Suarez even compared him to Liverpool legend Steven Gerrard, saying:
"I already said that he reminded me of Steven Gerrard, who was a teammate of mine at Liverpool...He has similar abilities. A box-to-box player, with punch, who can change the rhythm, who arrives well. I don't want to compare but the characteristics are similar."
Real Madrid are delighted with the Uruguayan and his versatility of playing in midfield and as a winger.
He only renewed his contract last year, ending in 2027, but interest in his services is intensifying.
Valverde demands a pay rise from Madrid president Florentino Perez for his contract to reflect his importance to Los Blancos.
Liverpool, Manchester United, and PSG have Valverde listed him in their priorities.
However, he is settled in the Spanish capital and wishes to stay.
The midfielder is grateful for the opportunity Madrid gave him when they signed him from Penarol in 2016 for €5 million when he was relatively unknown.
He has won the La Liga title twice and the UEFA Champions League during his time at the Santiago Bernabeu.
Valverde has made 168 appearances, scoring 14 goals and providing 12 assists.
Real Madrid are set to battle Liverpool for Borussia Dortmund teenager Jude Bellingham
Real Madrid and Liverpool are leading the race to sign highly sought-after Dortmund teenager Bellingham.
According to MARCA (via ManagingMadrid), BvB have slapped an astounding €150 million price tag on the English midfielder.
Bellingham, 19, has been a revelation for Dortmund, making 22 appearances, scoring nine goals, and providing three assists.
Ancelotti is rebuilding his Real Madrid midfield following the signings of Eduardo Camvinga from Stade Rennais and Aurelien Tchouameni from AS Monaco.
Meanwhile, Jurgen Klopp has been a long-term admirer of Bellingham, and the Reds need to revitalize their stagnating midfield options.
Bellingham brings versatility and unpredictability to Dortmund and has shown maturity beyond his years.
He became the youngest captain to score in a Champions League match in the Bundesliga side's 4-1 win over Sevilla on 5 October.
The teenager is currently at the 2022 FIFA World Cup with England and scored his first international goal in the side's 6-2 thrashing of Iran in their opener.