With momentum on his side, Cash thinks that the 25-year-old will win another "half a dozen" Grand Slam titles, including Wimbledon.
"In the fifth set against Djokovic, Murray was complaining that his legs felt like jelly. This was caused by fatigue but also nerves and pressure. Winning a first Grand Slam will certainly help that," said Cash.
"I think he will win half a dozen Grand Slams. I think he will certainly win the Australian Open and Wimbledon, possibly even next year.
"And he will be number one in the very near future."
Cash won the SW19 title in 1987.