Wilder's departure is expected to be formally announced later today.
A press conference ahead of Sunday's game with Leicester City was scheduled for 5pm on Friday, but it was cancelled about fifteen minutes before it was due to take place.
Various reports suggest that former Barnsley and Leeds United head coach Paul Heckingbottom will take temporary charge for the game.
Wilder, 53, a boyhood fan of the Blades and a former player, took charge of his hometown club in the summer of 2016 and has presided over two promotions in his eventful reign at the club.
But after four outstanding campaigns of progress, United have endured totally contrasting fortunes in a nightmare 2020-21 campaign which is highly likely to end in relegation from the top-flight.
They are 12 points adrift of safety with only 10 matches remaining.
Despite a fraught season, Wilder is widely viewed to be one of the most successful managers in the club's history, having led them out of League One in his first year at the club in 2016-17 and ending their 12-year exile from the top-flight in a fabulous 2018-19 season.
Those feats continued last term when he led the Blades to ninth last season - their joint highest league placing since 1991-2.
Only Manchester City's Pep Guardiola (134) and Liverpool's Jürgen Klopp (117) have won more league games under a single manager in England's top four tiers than the Blades under Wilder, who has managed 94 in his spell at the club.
Speaking about his future recently, Wilder tellingly said that he did not know if he would be at Bramall Lane next season after being questioned about it, but added that he would like to remain 'if the club 'stick to the plan.'
It indirectly alluded to some tensions behind the scenes at the club following an awful campaign which also saw the club fail to add to their options in the January transfer window.
Wilder also recently referenced the need for the key players in the squad to remain together if the club were to have the best chance of reclaiming the top-flight position that they are likely to relinquish this Spring - and also spoke about the importance of infrastructural improvements.
“The plan was always to leave a legacy, change things off the pitch, stick with the players we’ve invested in, and try to add a few,” he explained.
“I want people to say, ‘He was all right, him.’ I want to put the club in a better position than I found it in 2016.”