The young Murray from Dunblane, Scotland, was "quite pale", recalled the Serbian, known as "The Joker" for his wisecracks.
Back then, they were playing on the juniors' circuit "just trying to play tennis and enjoy the game," Djokovic said. Little did either know that later in life they would keep running into each other on the biggest stages of world tennis.
Today, Djokovic and Murray meet for their third grand slam final at the Australian Open. It is the latest rematch in a rivalry that Djokovic describes as unique because they have known each other since childhood.
"It's nice to see somebody that you grew up with doing so well," the 25-year-old Serbian player said yesterday.
"We know each other since we were 11, 12 years old. I guess that adds something special to our rivalry."
Djokovic rose to stardom first, winning the 2008 Australian Open at the age of 20. Now, the No 1 ranked player owns five grand slam trophies and is aiming to become the first man in the Open era to win three in a row at Melbourne.
The third-ranked Murray is the latest addition to the so-called Big Four of men's tennis, which also includes the No 2 Roger Federer and the 11-time grand slam winner Rafael Nadal. The group has combined to win 33 of the last 34 grand slams.
Murray is striving for his second grand slam title after winning at the US Open, where he beat Djokovic in the final to end a 76-year drought for British men at the majors.
Murray's road to the final in Melbourne included one of the tournament's highlights - a five-set win in the semi-finals over Federer, a 17-time grand slam winner. It was Murray's first victory against Federer at a grand slam event and so physically draining that Murray was too exhausted afterward to crack a smile.
"It [was] a long, long match. It's a very late finish. I'm tired," said Murray, when asked why he seemed so subdued. During the intensely tactical and physical match, Murray served a stunning 21 aces against the Swiss player.
"I don't want to be wasting any energy, because I'll need all of it if I want to win against Novak," he said, adding that despite his lack of emotion he was pleased.
"Obviously, I was happy. It was a tough match."
Murray reached the Australian Open semi-finals last year, losing to Djokovic. He has made the Melbourne finals on two previous occasions, losing to Federer in 2010 and Djokovic in 2011.
Before arriving in Melbourne last year, Murray teamed up with the tennis great Ivan Lendl whose coaching has helped produce a new aggressiveness in Murray and a willingness to take chances on court.
It was under Lendl's tutelage that Murray made his breakthrough, winning a career-changing gold medal for singles at the London Olympics and then riding a wave of confidence to win his first major title at the US Open.
He expects a long, tough fight from Djokovic, who beat the No 4-seed David Ferrer in a Thursday semi-final, which gave the Serbian an extra day to rest and recover for the final.
"Every time we play each other it's normally a very physical match," Murray said.
"I'll need to be ready for the pain. I hope it's a painful match - that'll mean it's a good one."
"Every time we played ... It was always long matches, physically very demanding," said Djokovic, who shrugged off the idea that his extra day for recovery would be a factor in the final.
"He's considered one of the physically strongest and fittest guys around. So I'm sure he's going to be fit," said Djokovic, who played one of the tournament's other thrillers in the fourth round, when he needed five hours to beat Stanislas Wawrinka, another inspired Swiss player, in five sets.
Another tennis great, Andre Agassi, thinks otherwise.
Agassi, an eight-time grand slam winner, was in Melbourne on his first trip back to the tournament since his loss to Roger Federer in the quarter-finals in 2005. He will be taking part in the men's pre-final ceremony.
During a news conference ahead of the Murray-Federer match, Agassi correctly forecast that Murray would win. He went on to predict that Djokovic had the physical advantage going into the final.
"Two days off, going into it fresh, going into it ready is a big difference," Agassi said.
"I probably give the edge to Djokovic in the finals."
Asked how he would have tried to beat Djokovic, Agassi joked: "I would have probably gotten in a fight with him in the locker room before the match. I might have had a chance."
* Associated Press