Pique has spent a large portion of the week travelling to Madrid due to the involvement of his company Kosmos in the revamped competition of tennis' premier international team event.
LaLiga leaders Barca make the trip to rock-bottom Leganes on Saturday and Valverde has been speaking with Pique about his extra-curricular activities.
Valverde: "We have complicated, difficult matches coming. We have to be focused because from January onwards, we will depend a lot on the results from this month" pic.twitter.com/Z2StjnMq8c— FC Barcelona (@FCBarcelona) November 22, 2019
"I have talked with him about this issue and I see him as being focused," head coach Valverde said.
"If I don't think he's focused enough someone else will play. If he arrives in condition, he will be on the list. He has issues outside of football. Players are always blamed if they don't do anything else and only know football."
Asked if Pique has permission to travel to Madrid again on Friday, Valverde replied: "If he travels, you will see if we gave him permission. We have to leave him alone, Saturday we have an important game."
Valverde also insisted he is happy with the work of close-season signing Antoine Griezmann after it was suggested he performs better for France than for Barca.
Griezmann has four goals and three assists for Barca in 11 LaLiga appearances this term and Valverde says the forward is offering plenty to the team.
"I look at my team, what matters to me is how I see the team," he added. "I know there are many eyes on Griezmann but he is giving us many things in terms of work, goals and clarity of play. We think he can give us more."
Ousmane Dembele has had a stop-start season for Barca but was involved against Slavia Prague and Celta Vigo before the international break.
Valverde wants to see the exciting France forward get a long run of games under his belt.
"I think it's important he has continuity in his daily work and gets playing time," he said. "Since his first injury last season against Getafe, trying to get him back quickly has been counterproductive.
"He's had several relapses or different episodes with different muscular injuries and hasn't been able to perform the way he would have wanted.
"We hope we can start getting some regular rhythm."