"He has done a great job and Andy is a tremendous talent. Nothing he does will really shock me." Annacone suggested that for a player of Murray's "tremendous" ability, featuring in a major final like the Australian Open should not be the pinnacle of his career, but a springboard to even greater achievements.
He said: "Pete was the one who told me that, as player, after you get in the situation where you win a grand slam tournament or get to the finals, you make a sub-conscious decision what you want to get out of your tennis career.
"That will be up to him [Murray]."
Annacone is confident it will be a decision the teenager will be called upon to make sooner rather than later and, with a seeding of 15th in Melbourne, he is expected to make a serious bid for honours.
"Andy is a tremendously talented young player. He has beaten the best player in the world and the best players in the world," said Annacone.
"His talent level is definitely there to do some great things and he is capable of winning a grand slam tournament."