The 23-year-old goalkeeper has enjoyed a stunning season for the relegated Black Cats, also earning a call-up to the senior England squad, and is being eyed by several potential buyers.
Everton are reportedly the latest, but Moyes said: "It would need to be a really, really big offer.
"I have said all through the season that sometimes on your journey, you may have to sell to improve.
"But I have heard some really derisory sort of figures getting mentioned, and it wouldn't be any of those figures, I can tell you that."
Asked if the Washington-born keeper's price tag would be in the region of Â£30million, Moyes replied: "Yes."
Source : PA