Murray is the current holder of the US Open and Wimbledon titles, while his Olympic gold from last year makes him the world's most decorated player in terms of current Grand Slam titles held.
He is still placed behind Novak Djokovic and Rafael Nadal in the world rankings, but Wilander believes that the Scot is more interested in picking up Grand Slam titles than reaching the world number one spot.
"I'm not sure he will ever make world number one because I don't think that is what is the most important to him. Winning Wimbledon twice or the Olympic Games is more important to him. It's about winning grand slams, he's not trying for world number one," Wilander told Eurosport.
"That's what the media and the public rank players on but not what players measure their success by, as to be number one you have to win a lot of tournaments that are less interesting and the calendar is so full now. It's really tough. I really respect him for that and I think he'll win another five or six grand slams.
"When Murray is keyed up, in my view, he's the best player in the world. If he turns up with his head in the right place. Federer plays with artistry, Nadal fights with passion, and Djokovic strikes the ball. Murray is not as good as each of them for their particular skill and talent, but he has the whole package and that is his great strength. But only when he wants to."
Murray is currently bidding to defend his US Open crown and will face Florian Mayer in the third round at Flushing Meadows.