The teenage forward made a name for himself while on loan at League Two outfit Rushden and Diamonds last season, and Blades boss Neil Warnock was prepared to sell him to the Iron.
But the player has rejected a move to North Lincolnshire, according to Warnock.
He said: "Billy has turned down the offer, and we have told him he doesn't have to go.
"We are in the process of offering him a new contract, and if he signs we will let him go out on loan.
"I thought Scunthorpe would be a good move for him, playing at that level, and £100,000 was a realistic offer for Billy."