A tearful Murray revealed before the start of the event in Melbourne that he feared it could be his last tournament due to ongoing hip trouble.
He would love to say his goodbye to the sport at his beloved Wimbledon but, even though he went down fighting to world No 23 Roberto Bautista Agut in Australia, the odds on him being able to carry on look slim.
“All of Scotland and Britain wish him well and hopefully he can continue,” Montgomerie told The Scotsman as he prepared to play in this week’s Omega Dubai Desert Classic.
“He’s still ambitious and the will to win hasn’t left him, you can see that playing that five-set match in Australia. That’s amazing, the will to win. He’s still got that.
“If he’s got to go for more surgeries, go for it, because that is a very young age to stop [Murray is 31], a very young age to stop doing what you love to do.”
Montgomerie admitted that Murray’s situation had made him realise that he had been “very very lucky” to have been injury-free at the time he won eight European Tour Order of Merit titles.
“I didn’t miss an event through illness; I didn’t miss an event through injury,” he added. “Most sportsmen have a series of months off and I was very, very fortunate to stay very healthy during that time.”