Murray won his sixth title of the year in Valencia on Sunday
Andre Agassi believes Andy Murray will win multiple Grand Slams once the Scot wins his first, insisting "the floodgates will open" for the Briton.
The 22-year-old British number one is the only player in the world's top five not to have won a Grand Slam.
But following Murray's victory at the Valencia Open, Agassi said: "He has a self-inflicting tortured spirit about him when he's on the court.
"The last 18 months he's learned how to use it. He needs to stay with it."
Murray's victory in Valencia, courtesy of a 6-3 6-2 win over Russia's Mikhail Youzhny, was his sixth title of the season.
However, his failure to win one of the four major titles of the year will have been a big disappointment, especially as he was one of the favourites to triumph at the Australian and US Opens, exiting in the fourth round at both.
His best Grand Slam finish to date is as a losing finalist to Roger Federer in the 2008 US Open, while he reached the semi-final of Wimbledon this year.
"I think he'll win multiple Grand Slams," said Agassi. "It's been my prediction for a while.
He shouldn't get hung up on results
"This year was disappointing for him. I know he was on the verge in a couple of grand slams with the hopes of doing it. He just needs to stay with it.
"He's proved that he's a strong person. My advice? To keep getting better. Every day's an opportunity to get one day better.
"He shouldn't get hung up on results. Results are a by-product of your commitment and work ethic and not cutting a corner."
Meanwhile, Agassi believed tennis should be proud of its anti-doping progress and said drug testing was now watertight.
The 39-year-old shocked the tennis world with recent revelations that he failed a test for crystal methamphetamine in 1997 and lied to escape suspension.
In his new autobiography, the eight-time Grand Slam champion admitted he lied to tennis authorities about his use of crystal meth, claiming he had taken the banned drug accidentally.
His explanation was accepted and he escaped punishment at the time, but Agassi now believes drug cheats would get caught.
He said: "(In 1997) we were at the infancy of drug testing. It's a very sophisticated approach now.
"This was pre-era of sensationalising drugs in sport and, as a result of tennis pushing itself forward to protect its integrity, we reached out to the World Anti-Doping Association two years later and they've been a fabulous partner who've done a tremendous job in protecting that integrity of keeping drug cheaters out of the sport.
"They've tested me specifically 150 times. Our sport should be proud of how we've moved forward through this day and age.
"I don't think it's so easy, not when you're getting tested 15 or 20 times a year. It's a very sophisticated approach now.
"It's thorough, it's random, urine and blood, and any initial positive test is run through a process."