Salford-born Hogan has been a player on Blades manager Chris Wilder’s radar for some time.
Villa recently gave the forward the green light to discuss a move away from Villa Park, which alerted several Championship clubs including United and Bristol City.
The Blades have leapt ahead in the race to sign the 26-year-old – who joined Villa from Brentford in the mid-season window two years ago for a fee of £9m, potentially rising to £12m.
The Republic of Ireland international went on to score six times in 37 games during the 2017-18 season, but has fallen out of favour in the Midlands this season.
Hogan, who spent a spell early in his career at FC Halifax Town, would supplement the Blades’ earlier January loan signings of Cardiff City forward Gary Madine and Everton midfielder Kieran Dowell.
The deal is set to be completed on Wednesday