The striker was left out of the club's pre-season friendly against Eintracht Frankfurt earlier this week, with manager Uwe Rosler quoted by the Yorkshire Evening Post saying his exclusion was a precaution, but he was not injured.
Sharp signed for Leeds a year ago from Southampton, but scored just five goals, frequently played as a substitute, and failing to get a run of games. His strikes included winners against Middlesbrough and Huddersfield.
The Sun report Sharp is to leave Leeds' pre-season tour of Austria to clinch his move to the Blades. It is also claimed he will get a pay off to make up for the drop in wages.
It will be Sharp's third spell at the Blades, who have resisted suggestions Jamie Murphy could head the other way.
Sharp will link up with former boss Nigel Adkins, who previously managed him at Scunthorpe and Southampton.
What next for Leeds?
Sharp is too good a striker to be wasted on the bench, but does not appear part of Leeds' plans, and so letting him go makes sense. His frustration was evident last season, and so getting a £500,000 fee for him is a practical solution.
Leeds have invested in signing Chris Wood from Leicester, and also have alternatives in Steve Morison, Mirco Antenucci and Souleymane Doukara.
There remains a chance they take a flier on another striker, especially with Wood already picking up an injury. Cardiff's available striker (as reported by The BBC) Adam Le Fondre is one possible option.