The Daily Mail report that Bruce, 25 and son of Sunderland boss Steve, was all set to join the Blades earlier this week when the move collapsed because the two clubs could not agree how the £200,000 fee should be paid.
That alerted Leeds and they quickly agreed a similar fee with the Tractor Boys, rising to £300,000 based on appearances.
The Republic of Ireland international defender, who played 127 games in four years at Portman Road after signing on a free transfer from Birmingham City, is set to undergo a medical on Thursday morning and then complete the necessary paperwork.