According to Spanish radio RAC1, the board of directors of Barca will have a meeting on Monday to discuss Valverde's future with the club after the 3-2 loss to Atletico in Supercopa semi-final.
Valverde are booed and jeered by the crowd at the King Abdullah Sports City in Jeddah during the semi-final against Atletico.
Messi and Griezmann give Barca 2-1 lead but Morata's penalty and Correa's goal in the last 15 minutes ruin Barca's hopes to move into Supercopa final again.