Iron boss Brian Laws had hoped to secure the player's services on a season-long loan, but Blades boss Neil Warnock rejected an initial approach - saying that he would prefer the player to go to a League Two side as he would get more first-team football.
Laws has insisted publically that he is still keen to secure the player's services, but Warnock could opt to send Sharp to the basement division with Bury.
And Warnock has a soft spot for the Shakers, having previously managed them.
Laws is still hoping to get a positive response from the Blades, but insists he has other targets to bring in ahead of Saturday's season opener at Brentford.
He told the Scunthorpe Telegraph: "I'm hoping to get a response about the enquiry for Billy early this week.
"It is a situation we are hoping happens, but if it doesn't then we've got to look somewhere else and I've already spoken to other managers about different strikers."