The Fir Park boss was linked with the job following the departure of Danny Wilson and the League One side have now formally made their interest known to the Lanarkshire club.
It is understood McCall is keen to speak to the Blades and that Motherwell chiefs will grant permission for talks to take place.
Chief executive Leeann Dempster told STV: "I can confirm we had an approach from Sheffield United regarding Stuart McCall last night."
Dempster has already stated the club would not stand in the way of McCall sealing a move elsewhere.
McCall was previously linked with moves to Blackburn and Burnley and, most recently, with Doncaster Rovers.
He has found himself in demand after guiding Motherwell to second place in the SPL.
Speaking on Friday about reports linking him with a switch to Bramall Lane - where he had spells as a player and assistant manager - McCall said: "You can't stop speculation.
"I've never once looked to go elsewhere, whether as a player, coach, manager.
"If, for example, Sheffield United wanted to speak to me, the club and the board have always been open with me as I have been with them."