The Blades will be announcing the departure of Slavisa Jokanovic today [Thursday] with the club 16th in the English Championship.
According to The Scotsman's sister paper The Star, Heckingbottom is the favoured candidate ahead of former Hamilton Accies manager Alex Neil.
Neil has been out of a job since leaving Preston North End and has admirers amongst the United board.
However, owner HRH Prince Adullah bin Musa’ad bin Abdulaziz Al Saud will give Heckingbottom the opportunity, the former Easter Road boss having filled in as caretaker following Chris Wilder's departure last season.
The 44-year-old had a 32-game spell at Hibs between the 2018/19 and 2019/20 campaign after roles at Barnsley and Leeds United.
Sheffield United were expected to be challenging for promotion and won during the week, a game which saw Scottish midfielder John Fleck collapse.