The Evening News’ sister title, the Sheffield Star, is reporting that an announcement confirming the split could be made later today.
Wilder and a Blades player were due to fulfil media duties via Zoom this morning but the club told journalists the player would not be appearing as scheduled, leading to rumours something was going on behind the scenes.
The 53-year-old has been in charge of United since 2016, leading them out of League One and into the Premier League within three years.
Wilder led the Blades to ninth in the table last year but a disastrous run of results has seen them pick up just 14 points from 28 games and as things stand they are 12 points from safety with just ten games remaining.
Former Hibs head coach Paul Heckingbottom could take the team for this weekend's match against third-placed Leicester City. The Yorkshireman joined the coaching set-up at Bramall Lane in July last year, and coaches the club’s Under-23 team.
Heckingbottom succeeded Neil Lennon at Easter Road in February 2019 but was sacked in November the same year. He oversaw 32 matches, winning 12, drawing ten, and losing ten.
He was sacked following a 5-2 Betfred Cup semi-final defeat by Celtic with Hibs sitting tenth in the Scottish Premiership table, and was replaced later that month by Jack Ross.
Prior to his spell in the Capital he had managed hometown side Barnsley, and Leeds.