PFA player of the year nominee Bale, 23, has been linked with a host of sides, including Spanish duo Real Madrid and Barcelona, after scoring 28 goals for club and country this season.
In recent seasons the likes of Dimitar Berbatov and Luka Modric have been prised away from Tottenham in big-money moves to Manchester United and Real Madrid respectively.
But Walsh feels Spurs should resist any temptation to cash in on Bale, just as they did over Modric when Chelsea were interested in the midfielder two summers ago.
"He has three years left on his contract so Tottenham are in a position where they can say, 'You're not going anywhere. We are going to keep you'," said Walsh.
"(Chairman) Daniel Levy has been quite hard-nosed on a couple of other occasions in the past so I don't think Tottenham are just going to roll over.
"He didn't let Modric go that summer and that might be what they have to do with Bale."