Hogan has been on loan at Bramall Lane from Villa since January, scoring one goal in seven appearances.
Manager Chris Wilder is looking to improve his squad ahead of the Blades’ first season back in the Premier League in 12 years.
United secured promotion to England’s top flight with a game to spare. They brought their last Championship campaign for at least a year with a 2-2 draw at Stoke City on Sunday.
Wilder is expected to stick with the 3-5-2 formation that has served him so well over the past three years. During that time the club has been promoted twice.
For the two striker positions Wilder currently only has two options – captain Billy Sharp and David McGoldrick. He spent large parts of this term with five forwards in his squad.
That is why Wilder is looking to potentially sign Hogan permanently. The 51-year-old is also considering a similar deal for Gary Madine, who is currently on loan from Cardiff City.
How much would Hogan cost?
The Villans signed the 27-year-old from Brentford in January 2017 for a fee that could eventually rise to £12m (BBC).
Unfortunately for Hogan his time at Villa Park turned out to be less than successful. The forward scored 10 goals in 61 appearances in two years as he was increasingly sidelined by former manager Steve Bruce.
When Bruce was sacked in October, Hogan publicly criticised the 58-year-old for not allowing him to join the Blades in the summer, but then signing Tammy Abraham on loan from Chelsea.
Previously the Republic of Ireland international had been prolific at Griffin Park. This is despite spending the best part of two years out with a cruciate ligament injury.
During Hogan’s time with the Bees he scored 21 goals in 36 matches.