The Mirror says Schmeichel, who has done his coaching badges, is set to throw his hat into the ring to succeed David Weir.
Ex-Everton defender Weir got his marching orders after just four months at Bramall Lane.
The Blades currently sit bottom of League One, having won only once in the league this season and suffered a 3-2 loss at Coventry this weekend.
Former captain and under-21 coach Chris Morgan is in temporary charge.
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