The former Wales international wrote in his column in The Mirror that the winger must quit White Hart Lane if he is to become one of the best players in the world.
"Tottenham fans will not thank me for saying this, but Gareth Bale will have to quit Spurs if he is to fulfil his potential," wrote Savage.
"Tottenham know that, one day, they may not be able to hang on to Bale because, in my opinion, he is already among the top six players in the world – and his stock is rising.
"For Bale to reach the next level, and become a superstar in his own right, I'm afraid he will have to move from White Hart Lane."
Bale scored both goals for Spurs as they overcame Newcastle United 2-1 at home on Saturday.