"But I hope the club do not just put the money from Bale in the bank," Sheringham told the Sunday Mirror.
"If the cash is re-invested, then the fans will be happy.
"With the money they get from Bale, Tottenham could easily buy at least two or three more players in the £20m bracket and they will really improve the squad.
"And I am sure the supporters will wish Bale all the best.
"His best chance of winning honours is at club level. With all due respect to Wales, it is going to be very hard to be successful because they rarely reach the finals of major competitions, such as the European Championships or the World Cup.
"Real are special and I think it is a chance that Bale has to take if he can move there. When they come calling, you have to take advantage of it."