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The Rovers gaffer is a big admirer of the ex Scunthorpe attacker and has told The Sheffield Star that they have been in contact with Sheffield United regarding a move for the 23-year-old.
It could be said that Sharp hasn't played to the best of his abilities since returning back to Beautiful Downtown Bramall Lane two summers ago, and has only bagged a mere 12 goals in all competitions.
O'Driscoll said: "After we got word about him, we made an inquiry, as you do, to see what the situation was with him," said the Rovers boss.
"We contacted Sheffield United, asked some questions - about the length of his contract, the wages he's on, whatever transfer fee they might want or if they were wanting to loan him out.
"They're the two conversations we've had.
"People mention a player like that and we're probably talking millions of pounds and I don't know where we are going to get that sort of money,. We are sort of scrabbling around right now."