The former Manchester United goalkeeper looks ready to take the plunge in management after completing his coaching badges and has been linked with the vacant position at the League One club.
The Blades, who are surprisingly bottom of the table, sacked manager David Weir on Friday after their disastrous start to the season.
Schmeichel addressed rumours that he could take the job on Twitter by saying: "I can see that I've been linked with the vacant managers job at Sheffield United.
"This is not my doing, I have not applied for any jobs, but it's great to be associated with such a great football club."
Former Derby manager Nigel Clough, Leyton Orient boss Russell Slade and ex-Blade and current Motherwell manager Stuart McCall have all also been linked with the job.
The Blades have won just one of their 11 league fixtures this term, with that coming on the opening day, and currently sit bottom in the table with just five points.
Former Scotland and Everton defender Weir, 43, was only appointed in June, taking up his first job in management.
But his stay at Bramall Lane did not last long having been relieved of his duties along with assistant boss Lee Carsley.
Weir replaced Danny Wilson in the summer but endured a baptism of fire in his first management role, losing nine the 13 matches he was in charge of in all competitions.
Saudi Arabian Prince Abdullah bin Mosaad purchased 50 per cent of the club's share from owner and chairman Kevin McCabe last month and gave Weir his full backing.
But the club's fans have consistently expressed their concern at such a poor start to their third season in the third tier, which has seen the Blades lose six of their last seven games.