Bale has been linked with moves to Barcelona and Real Madrid in recent months, and Sheringham, who had two spells at Spurs between 1992 and 2003, thinks that the Welsh international should jump at the chance of moving to Spain.
"If Barcelona or Real Madrid come in for Gareth, it's something he'd have to think about," Sheringham told The Mail.
"I think he will do well wherever he plays. Anyone that can run with the ball at pace will excite you, he is very much like a young Ryan Giggs."
Bale was part of the Tottenham side that drew 1-1 with Manchester United on Sunday.