Edberg, who won the British Grand Slam twice during his playing days, admits that he expects Murray to triumph at more major tournaments on his way to moving to the top of the rankings.
"I believe Murray can still win a lot more Slams. He's good enough and young enough," Edberg told BBC Sport. "He's got a few really good years ahead of him.
"He's proved he can play well on grass and there is no question why he can't do it again. It could be in his mind to be the number one player in the world. It's going to be tough to get that but that's probably something that can be achieved.
"He needs to produce the results for 12 months, but this could be a great start of it."
Murray is currently ranked number two in the world.