The 31 year old striker saw his bid by second placed Blades rejected by chairman Barry Kilby, believed to be 1.75M.
The former Norwich trainee netted a deal to the Lancashire club for £600,000 in February 2005, beating the Blades to his signature.
"Sheffield United made an offer for Ade that we have turned down," Clarets chairman Barry Kilby told the club's official website, www.burnleyfootballclub.co.uk.
"I don't want to talk figures, but they didn't meet our valuation of the player and that's where we stand at the moment."
It is believed that Ade will sign by the end of today, we'll believe it when we see it!