United are looking to add at least one new midfielder to their first-team squad by the end of the summer, with the 30-year-old the latest player of interest.
A five-year contract has been tabled and turned Casemiro's head.
Speaking outside his club's training ground on Thursday, Valverde was quizzed on the future of his midfield teammate and the interest from United.
"He hasn't said anything," the Uruguayan said. "I don't know anything. Of course [I want him to stay]."