Shearer, 40, endured a tough baptism as gaffer, failing to stop his beloved Newcastle United falling through the Premier League trapdoor during an eight-match stint at the end of the 2008-09 season.
Speed, who has taken over the Blades from Kevin Blackwell, said: "Alan has got too much to offer not to have another crack. He won't be too far away if the right offer comes along.
"He has definitely got the right attributes. You can tell straight away that he is very single-minded, very focused.
"That would stand him in good stead to be a manager and I don't think it will be too long before he gets a job."