Dutchman Cillessen, who is the second-choice keeper behind Marc Andre ter Stegen, has been linked with a move away from the Spanish giants, with Barcelona reportedly interested in bringing Liverpool stopper Simon Mignolet into the team.
Speaking after Barca's 1-0 defeat to AC Milan on Saturday, Valverde told reporters that he would be "very happy" if Cillessen opts to stay for the upcoming season.
"My idea is to have two good goalkeepers, the two we have now, Marc and Jasper," the manager said. "It's true that [Cillessen's] not played as much as Marc, but that's how being a goalkeeper can be.
"He knows what I think. I don't think he will be hard work if he stays, we are very happy with his professionalism and his attitude. We hope he stays with us and is happy [here]."
Barcelona have only won one of their three pre-season outings, with a penalty shootout victory against Tottenham Hotspur being followed up by a 4-2 defeat to Roma.