Olympic silver medallist Murdoch, the coach to Team GB’s newest Olympic champions, was a team-mate of Muirhead in Sochi and Vancouver, where she made her debut as a teenager.
Now 31, he believes Olympic gold could be just the inspiration she needs to push on and dominate the sport with her superstar rink of Vicky Wright, Jennifer Dodds, Hailey Duff and Mili Smith.
“She could definitely go on to be one of the greatest ever,” said Murdoch, who is from Lockerbie.
“She’s been around so long, she’s won World Championships and Europeans and now she’s got that Olympic medal, she’s done everything in the sport.
“She’s one of the most dedicated athletes you’ll ever see, never a day goes by when she doesn’t commit 100 per cent to training, and if you do that you’ve got to hope that you get your rewards.”
Murdoch admitted there were some tough questions after an eighth-place finish at the World Championships in Calgary, which meant the team needed to come through a stressful qualifying tournament last year to secure their Olympic spot.
They lost to minnows Turkey there before rebounding in style, while their run in Beijing has been far from simple.
They won five and lost four of their group games, advancing to the knockouts by just ten centimetres via a complicated formula known as the draw shot challenge.
And it didn’t end there, in the semi-finals against Sweden they found themselves four down after the first end, Murdoch admitting he then thought their hopes of winning were ‘less than ten per cent’.
He added: “Sometimes things are just written in the stars aren’t they?
“The conversations we had after the Worlds were tough and they needed to be tough. It was probably the most important thing we’ve ever done, because what’s come of that is ultimately this. Credit to them for picking themselves up, coming out and working hard to get this gold.
“They deserve every moment of this because the hard work they’ve put in in the academy, touring around the world, the sacrifices they’ve made personally.
“It was in their hands to go out there and deliver and show the skills that they had and by heck that was incredible.
“It was a perfect performance. The composure and the calmness was evident and you could just see all the girls were just so relaxed.”
National Lottery players are one of the biggest supporters of Team GB and ParalympicsGB winter athletes and raise more than £30 million each week for good causes including grassroots and elite sport. Discover the positive impact playing The National Lottery has at www.lotterygoodcauses.org.uk and get involved by using the hashtag: #TNLAthletes