David Weir was dismissed by the Blades on Friday, along with his assistant, former Derby County midfielder Lee Carsley, having only been appointed in the summer.
United are languishing in the League One relegation zone, with only five points from their opening 10 games.
Bookies have him as favourite for the role, ahead of the likes of Stuart McCall and current Blades Under-21 coach Chris Morgan, who will take caretaker charge of the first team this weekend. The 3-2 defeat to Coventry on Sunday won't have helped Morgan's cause and that result leaves United propping up the table after Tranmere's surprise win at Bradford.
According to betting expert Joe Ross from www.footyinsider.co.uk its not a one horse race though:
'Tony Pulis, Russell Slade and former Rams boss Paul Jewell are also in the running and United simply have to get their choice right. The club were in the Premier League not that long ago and have a fantastic fan base. We rate Clough - and had tipped Derby as outsiders for the Championship.
'But if you need a man to keep you up and are prepared to swop substance for style, Tony Pulis, who has never been reglegated would also be a safe pair of hands.
'Given that he shunned the Sunderland job though, it seems unlikley that Pulis, who lives on the south coast, would drop down two divisions and Clough has to be the main man.'