Stuart McCall is set to land the vacant manager's position at Bradford City after missing out to succeed Neil Warnock at Bramall Lane.
McCall will be grateful for Warnock's endorsement
BBC Radio Sheffield says Blades' chairman Terry Robinson has also ruled out ex-Fulham boss Chris Coleman.
Robinson said: "We didn't feel Stuart met the criteria necessary to get the club back into the Premiership."
"Chris has experience of managing in the top flight but limited experience in the overall context of football."
Sheffield United plc chairman Kevin McCabe had earlier hinted that McCall, who was Warnock's assistant, would be interviewed for the post.
Warnock had already given his backing to McCall, who became his right-hand man in 2004.
He said: "I think the club has to look and see if they want to go inside with Stuart, who is ready for management.
I'm looking for a new challenge to bring the sparkle back
"I think whoever comes in could take United straight back up."
BBC Sport understands McCall is to be named Bradford's permanent boss, taking over from caretaker David Wetherall, who was appointed following Colin Todd's departure in February this year.
McCall was a lynchpin of the Bradford side of the late 1980s which almost won promotion to the top flight before securing a move to Everton.
He then joined Rangers, where he won the Scottish title before returning to Valley Parade to help the Bantams win promotion to the Premiership under Paul Jewell.
McCall joined The Blades as a player in July 2002, combining it with a role coaching their reserves.
When he hung his boots up he stepped straight in as Warnock's assistant in 2004.
Warnock also believes The Blades could ride out the speculation surrounding the futures of players like Phil Jagielka, sparked by United's relegation.
He said: "I don't think the departures of one or two players will affect their chances, I can't see anyone being better than Sheffield United last year.
"A new manager will have a bit of leeway if things don't go so well right away from the start.
"But with new blood I think there is no way they are not going to get automatic promotion, so it's a great time for someone to get the job."