The Daily Mail reports that the Blades have opened an inquiry, with Morgan agreeing to step away from the club while the investigation takes place.
The manager has been absent from a number of games, and has not been seen in the dugout since September, when his side beat Lewes 1-0. In the meantime, his assistant, Luke Turner, has taken charge of the first team.
Concerns have been raised over Morgan's behaviour and his alleged treatment of certain members of the squad, per the report.
The coach previously managed Leicester for seven years and has also managed Burnley, prior to his move to Bramall Lane in February when he replaced Neil Redfearn.
The news comes just weeks after the tragic death of vice-captain Maddy Cusack, who passed away at her home on September 20.
Although the circumstances were not deemed to be suspicious, the cause of her death has yet to be established, with an inquest having been adjourned earlier this month.