"He could easily end up with between 800 and 1,000 Test wickets," said Walsh whose record of 519 wickets was broken by the spin king in Sri Lanka's first Test win against Zimbabwe in Harare on Saturday.
"To get 500 wickets in less than 90 Tests, I think he deserves whatever he gets," Walsh told Radio Jamaica.
"He has been a tremendous bowler for Sri Lanka and he is bound to get wickets as long as he is playing.
"His strike rate is phenomenal. He deserves all the credit he is getting."
Muralitharan is now poised for a lengthy battle with Australia's Shane Warne, who has 517 wickets, to hang on to top spot.
"He is younger and because he is an off-spin bowler, I think he will play a little longer than Warne," Walsh said.