The Englishmen has played well this season despite the Black Cats finishing bottom of the Premier League table.
Speaking on rumours about Everton's £15m bid for Pickford, Moyes said via BBC Sport: "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."
Moyes was then asked if Pickford's price range was around £30m, to which he replied: "Yes."