Wilder was only handed a new three-year contract at Bramall Lane in January but the 57-year-old’s future has now been plunged into doubt.
It comes after Sheffield United’s play-off final defeat to Sunderland at Wembley last month, leaving the Blades preparing for a second successive season in the Championship.
Reports say United’s seven-person board is now deliberating over Wilder’s future, with the former Boro boss having not yet received confirmation of the club’s decision either way.
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There are said to be splits in the boardroom as to whether Wilder is the best man candidate to lead Sheffield United forward after their play-off final defeat. Recruitment is said to be one particular source of tension.
After Sheffield United’s defeat at Wembley, with Sunderland’s Tommy Watson scoring the winner in stoppage time, Wilder said: “We’ve had the taste of Premier League, we know what a great experience it is and the experience that they’ll have next season.
“It’s going to take quite a while to get over this and we’re going to have to suffer and go through the pain.”
If Wilder does go, Sheffield United will join Boro, Bristol City and QPR in looking for a new head coach.
There also remains uncertainty at Leicester City, with Ruud van Nistelrooy’s future unclear as things stand.