The report suggests Liverpool had been willing to part with £85m this summer to add the 24-year-old Uruguay international to their ranks, but Real Madrid’s sale of Casemiro to Manchester United scuppered any potential of a deal.
Liverpool ended up acquiring Arthur Melo from Juventus on a short-term deal instead.
Valverde has scored three goals in six La Liga appearances so far this season.
He provided the assist for Vinicius Junior as Real beat Liverpool 1-0 in the Champions League final in May.
