The 17-year-old midfielder made his debut for the League One side last season against Rotherham United.
His first start for the Blades came on Saturday in their 2-1 defeat at home to Bristol City.
"It is incredible that he has only just turned 17," manager Nigel Clough told the club's official website. "He has had a terrific pre-season and is progressing really well."
United are back in action on Wednesday night when they host Mansfield Town in the opening round of the League Cup.