The News of the World says the Bramall Lane chief is on the brink of losing his job after a dramatic slump that has left the club floundering way off the play-off spots.
Blades fans have turned on Blackwell in recent weeks despite yesterday's 1-0 win over bottom side Peterborough.
The United bosses are desperate for a return to the Premier League and Shearer has growing support.
They believe he would be the talisman to breath life into a campaign that is in serious danger of being blown out before December.
They would back him in the January transfer window.
For his part, Shearer is keen to return to management after his brief spell in charge at Newcastle last season.