But Law, who has spoken to Warnock twice this week, is still hoping to convince him that North Lincolnshire would be a good destination for him.
He said: "Billy is a player we've been looking at and there are another couple we've enquired about.
"We're looking to strengthen in that area, but we're not going to panic.
"Certainly in the near future we want to bring another couple of players in, but we can't waste our money. When we get it we have to use it wisely.
"I've spoken to Neil Warnock twice, trying to resurrect the situation and he's having a think about it over the weekend and will hopefully give us an answer next week."
Sharp was on trial at Glanford Park last pre-season, and impressed in a pre-season friendly against Scottish giants Rangers.
He spent the second half of last season on loan at Rushden and Diamonds, where he netted nine times in 16 League appearances.