The Uruguay international has emerged as one of Carlo Ancelotti's star performers in the 2022-23 season with four goals and two assists from nine games in all competitions.
Valverde has been utilised in the middle of the park and right-wing by Los Blancos, who won the Champions League with the South American featuring prominently out wide last term.
Marco Asensio and Rodrygo have been kept at bay by Valverde in recent months, and he has now celebrated his sixth anniversary as a Real Madrid player.
Valverde emerged as a breakthrough talent in his native Uruguay with Penarol before joining Real Madrid Castilla in 2016, with Los Blancos paying £4.5m to secure his services.
However, things could have been very different for the midfielder, as he had supposedly been on the brink of a move to Arsenal before ending up in Madrid.
According to Spanish outlet AS - via football.london - Arsenal had taken notice of Valverde's exploits for Penarol's youth teams, and Arsene Wenger was offered the chance to sign him.
Valverde's agent is said to have flown to London in December 2014 to thrash out an agreement, and the Uruguayan had even trained with the Gunners before a move was made official.
In the end, Arsenal ultimately passed up on their chance to sign Valverde, who has since made a total of 157 appearances for Real Madrid since breaking into the first team.
The 24-year-old was loaned out to Deportivo La Coruna for the 2017-18 season before making a name for himself at the Bernabeu, and he has 10 goals and 10 assists to boast in Real Madrid colours.
The 43-cap Uruguay international has already won seven major honours with Ancelotti's side, scooping one Champions League crown, two La Liga titles, one Club World Cup, one UEFA Super Cup and two Supercopa de Espana titles.
Eight years after their supposed pursuit of Valverde, Arsenal are still on the lookout for midfield reinforcements after failing to bolster their ranks in the engine room during the summer window.
Mikel Arteta is working without Mohamed Elneny for the long-term due to a hamstring injury, and Thomas Partey had only just recovered from a similar issue before fears of another layoff were raised during the international break.
The injury-hit Ghanaian experienced knee discomfort before his country were due to take on France in an international friendly, and he has since returned to London Colney to undergo further assessment.
Partey is not expected to be nursing anything serious, but it remains to be seen if the midfielder will be fit to play in Saturday's North London derby against Tottenham Hotspur at the Emirates.