The centre-back has claimed a number of clubs are interested in him, with Manchester United reportedly among the frontrunners to sign the France international.
Umtiti's relatively low release clause of €60million has encouraged speculation he could leave, although Barca are thought to be keen to increase it by offering him fresh terms.
Valverde believes the 24-year-old is happy at Camp Nou and is confident he will commit his future to the club.
"I have not followed Umtiti's statements," he told a news conference. "What I understand, and I know, is that he is very happy here and we are very happy with him.
"We hope the negotiations will come to fruition and that he will be able to continue for many years here."
March 12, 2018
Captain Andres Iniesta has also been linked with a move away at the end of the season, with clubs in the Chinese Super League said to be ready to offer him a massive contract.
Valverde, though, insists the midfielder's future is not in his hands.
"I have not thought of any strategy for Iniesta to stay because I do not have to have any strategy," he said. "Andres knows what he wants and it's a personal decision."