Kane has been vocal in his desire to win trophies as he approaches in 28th birthday still looking for his first piece of silverware.
Both Manchester clubs and Real Madrid have been linked with Kane, who saw his side lose for an 11th time in the league at Leeds on Saturday, has been urged to consider his options.
Shearer said on Match of the Day: "If Harry wants an excuse then Tottenham and that team are giving him one. They didn't show up for the cup final, they didn't show up again today (against Leeds).
"If I was in his position then I would look to go elsewhere."