The Wimbledon champion played football as well as tennis when he was a teenager and was apparently offered a trial with Rangers.
He turned it down to concentrate on tennis but his mother Judy believes he would have been a success in football or any other sport.
Speaking as she helped to make the draw for the first round of football's Scottish Cup, she said: "For him, he has worked so incredibly hard for so many years and he is so dedicated to doing whatever it takes to get to the very top. I think his biggest strengths are his competitiveness and his incredible attitude.
"He was very co-ordinated as a young boy so it wouldn't have mattered which sport he'd chosen, he would have been able to do it pretty well, which is my whole argument about it starting at home, parents playing with their kids."
Ms Murray said her son's training and preparation should be an example to all young athletes.
"Nobody gets to the top of any sport without that kind of dedication and hard work. What Andy's success shows is that nothing's impossible. I hope that it inspires Scottish kids not just to take up tennis but to actually believe in themselves," she said.
"It is all about the mindset and the environment that you are nurtured and developed in. We have to be fostering all these things. Part-time commitment equals part-time results. He has put everything into it and he has got to where he has got to because of that. I think other athletes and other sports can learn a lot from that.
"Any athlete who has got to the top of their sport would tell you exactly the same thing."
Murray returned to the tennis circuit this week in Montreal for the first time since his Wimbledon victory over a month ago. He is preparing to defend his US Open title in New York later this month and his mother thinks his win in London will lead to more success.
"Wimbledon is the big one for all tennis players, particularly British. It is your home slam," she said.
"I would have expected some kind of sense of relief, you know, and maybe him to relax a little bit. But I actually think it has done the opposite. It will spur him on to want to do more."