Valverde collected his first trophy as Barça coach last weekend in the shape of the Copa del Rey, while he is on course for the first ever unbeaten season in a 38-game La Liga campaign.
But throwing away a three-goal Champions League quarter final aggregate lead against Roma led to uncertainty. Bartomeu even inadvertently fuelled the gossip with an off-hand remark when he referred to the club's winning mentality, 'be it with Ernesto Valverde or another coach'.
"[Exit speculation] is false, he has two years of contract and this is his project, we are very happy with him," Bartomeu is quoted as saying by Marca.
"I speak regularly with him, we have not talked about [him leaving].
"After what he did in summer, nobody can doubt Valverde.
"Rome was bad for everyone, none of the directors doubted Valverde at any time."
Barça can mathematically wrap up the Spanish title this weekend if they beat Deportivo La Coruña, who could also be relegated in the same game, or simply if Real Madrid and Atletico Madrid are beaten by Leganes and Alaves respectively.
It would be back to business as usual for the Catalans after losing the title to Real last season, but going unbeaten, something that Pep Guardiola and Luis Enrique could never do, would make it an extra special achievement.