The Premier League outfit are searching for a successor to Nigel Pearson who was sacked amid controversial circumstances earlier this month.
Ex-Celtic boss Martin O’Neill has already been linked with the post at his old club.
Old Trafford legend Schmeichal, 51, who played for United between 1991 and ’99, has not managed before and would have to deal with overseeing the development of his son Kasper – also a goalkeeper.
O’Neill, the current supremo of the Republic of Ireland, Scotland’s Euro 2016 rivals, was believed to be the club’s preferred candidate last week with some supporters keen to bring back the man who presided over the team’s most sustained periods of stability and success.
However, it is understood the club have yet to approach the Irish FA with their interest.