Ever since stints with Penarol and Deportivo La Coruna as a youngster, Valverde has established himself as an important member of the Los Blancos squad.
Largely playing in either central midfield or on the right flank, a total of 19 goals and 15 assists have been contributed from 209 appearances in all competitions.
The most recent of those strikes came on Sunday evening, the Uruguay international scoring the equaliser as Madrid came from behind to record a 2-1 victory over Real Sociedad at the Bernabeu.
That made it five successive wins in La Liga for Carlo Ancelotti's side, yet the leveller versus a rival came from a player who was frequently linked with an exit before the end of August.
Given the acquisition of Jude Bellingham from Borussia Dortmund, there was a perception that the 25-year-old could be sold due to the array of options at Ancelotti's disposal.
Liverpool, Manchester United and Chelsea were all linked with an approach for Valvarde in a deal that would have cost in excess of £80m.
A report claimed that Valverde had regreted not taking more interest in a switch to the Premier League at a time when each of the three clubs in question were strengthening their respective midfield ranks.
However, as quoted by transfer expert Fabrizio Romano, Valverde has insisted that he was never looking to depart Spain's capital ahead of the close of business for another four months.
Speaking after Sunday's encounter with Sociedad, Valverde said: "Premier League offers? I have the ability to play for Real.
"The day I don't feel like that, I'm probably going to look for another solution or Real itself will look for one for me."
Romano has claimed in the past that Valverde, who has four years left on his contract, has had at least two proposals to make the switch to England.
Valverde will be hoping to retain his spot in the starting lineup when Real play host to Union Berlin in the Champions League on Wednesday night.