It is two months since the Blades parted company with Chris Wilder who led the club from the third tier to the Premier League following his appointment in May 2016.
Heckingbottom stepped up from his role working with the under-23 side to oversee first-team duties until the end of the season.
The relegated Blades are set to make an appointment sometime after their final game of the campaign at home to Burnley on Sunday, with former Watford and Fulham manager Slavisa Jokanovic, Oostende head coach Alexander Blessin and Club Brugge boss Philippe Clement reported to be on the club’s shortlist, along with Heckingbottom.
The 43-year-old thinks a decision should come sooner rather than later.
“I personally, and I am not speaking for anyone else, would like a quick appointment for the last game or straight after the last game,” said Heckingbottom.
“Because then you can start laying the groundwork and the manager can start convincing players to stay, some with their heads turned, making decisions on player ins and outs and that’s really important for that stability.
“It’s the start of a new era, the fact that I have been in this position now quite a long time since Chris left might have done everyone a favour in terms of everyone being ready and champing at the bit for this period and what it’s going to look like.
“And if it’s half as successful as what Chris’s was then the club’s going to do fantastically well again.
“We need that call now and we need that decision, in terms of the club, the squad and keeping it together. People need that clarity and need to know what they are doing.
“The ball can’t stop rolling, we have to keep pushing forward because there is next season to plan for and we are wanting a strong start.
“New era, new appointment and sooner rather than later to take all the positives and the good things into next season. We want to make a strong start next season.”
Despite being named on the shortlist by chief executive Steve Bettis, Heckingbottom is likely to return to his role with the under-23 squad.
But asked if this 10-game spell in charge had whet his appetite for a return to management, the former Barnsley, Leeds and Hibernian boss said: “Nothing has changed in the short term, I didn’t come here to be a manager. I came in to work with the young players and I’ve really enjoyed that.
“Long term yes I will do it again, I know I will. When that happens, I don’t know.”
The Blades will check on the fitness of George Baldock ahead of Sunday’s match. It is hoped the defender will be able to be involved on Sunday despite missing the midweek defeat at Newcastle because of hamstring discomfort.