Boothroyd only took charge at the end of last season after being appointed to replace Chris Coleman and had enjoyed a bright start to the campaign.
However, the Sky Blues have won one just once in their last 16 Championship matches and were beaten 1-0 at home by Hull City at the weekend.
That result left Coventry in 19th position in the table, seven points outside the relegation zone.
Shearer's name is in the betting to replace Booyhroyd, along with Chris Hughton, but I don't think the former Toon number nine has the bottle for the job.
It is now almost two years since Newcastle's relegation and Shearer's horror time in the Toon hot-seat ... EIGHT GAMES and only FIVE POINTS.
And I don't think he is over it yet.
Jobs come and go and all we've heard from the 'GOALden Boy' is "I don't want to be considered".
Does he have a lack of confidence in his managerial ability? I honestly think so.