News Of The World insist 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.
Shearer is keen to return to management after his brief spell in charge at Newcastle last season, and the Blades job would interest him, but he wants the challenge of the Premiership and Bolton could well be right up his street.
"He's desperate to get back in," said a source close to the former England captain. "He waited for Newcastle and it didn't happen.
"Now he wants another club. He has the hunger and he is just waiting for the right club with the right ambition."
Shearer still has his television work with the BBC but, as with the Toon job, they would let him move on.
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