Motherwell on Tuesday confirmed the League One side had made an official approach to speak to McCall.
The 48-year-old recently signed a new two-year contract and has consistently declared his satisfaction with working at Fir Park, turning down initial approaches from the likes of Burnley and Blackburn last season.
But Sheffield United are a club close to Leeds-born McCall's heart given his five years at Bramall Lane as player and coach and he is keen to talk to the Blades. The Motherwell boss had been due back from a club trip to Benidorm on Thursday.
Motherwell are working to persuade McCall to stay but chief executive Leeann Dempster last week stated the club would not stand in his way if he wanted to move on.
MK Dons manager Karl Robinson and former Middlesbrough boss Gareth Southgate have also been linked with the Blades job but McCall appears to be the number-one choice.
Former captain Chris Morgan took charge at United on a caretaker basis after Danny Wilson lost his job in April but United lost out to eventual play-off winners Yeovil in the semi-finals.
Speaking last week, McCall said: "There's not a part of me desperate to go. I'm not seeking out avenues to get away. If this is all speculation and nothing happens, then that's fine. I've not got a deep desire to leave this club because I'm having a great time here."
McCall has led Motherwell to the Scottish Cup final, Champions League qualifiers and a third and second-placed finish in the Clydesdale Bank Premier League in his two-and-a-half years at Fir Park.
But the former Scotland midfielder faces a rebuilding task ahead of their latest European campaign with goalkeeper Darren Randolph having signed for Birmingham and former Sheffield United midfielder Nicky Law deciding to move on.
- Sports & Recreation
- Sheffield United