Roger Federer and Novak Djokovic look destined to collide for the 46th time before they leave Melbourne, where they own a total of 11 titles. While history favours the Serb, his left hip may not.

At the end of the first week, they look in good shape to get out of the fourth round on Monday and stay on course for just a fourth semi-final showdown, where Djokovic has prevailed 3-0 on his way to winning a record six titles.

Federer’s only win over him here was 11 years ago in the fourth round but he is the defending champion. Above all, he is Federer, having reinvented himself at 36 like no other player in the history of the game surely could have done.

In the cool of the evening on day six – after a three-day heatwave that scorched the field and common-sense thinking – Federer took under two hours to beat Richard Gasquet for the 17th time in 19 matches. That pitches him into what should be a straightforward win over the unseeded Hungarian Marton Fucsovics, a three-sets winner over the similarly lightly regarded Nicolas Kicker of Argentina.

Djokovic put a shaky start to the tournament behind him, dismissing the 21st seed, Albert Ramos-Viñolas for the loss of seven games in two hours and 21 minutes. He has a tougher challenge in the next round against Chung Hyeon, who became the third South Korean to reach the fourth round of a slam after he surprised everyone but himself by upsetting the fourth seed, Alexander Zverev, in five sets.

Djokovic was not worried about needing courtside treatment for his left hip. “I wanted to use the medical timeout because I needed it,” he said, “but at the same time I knew it was nothing major that could potentially raise the question mark on whether I can continue playing or not.”

That possibility has hung over him since the start of the tournament but has centred on his right elbow, which kept him out after he went out of Wimbledon on day nine last summer and almost prevented him from returning to Melbourne, where he has had so much success.

He was a little defensive when pressed on the nature of the injury. “I played a long match against Gaël [Monfils] a few days ago. This didn’t happen too many times in my career that I have maybe some tension in the muscles or whatever, some kind of physical challenges. I’ve never faced a situation where I didn’t compete for six months. That’s why I’m forced to be very cautious of what happens day to day, to be dedicated to my body and training.”

Nobody dedicates as much time and energy to keeping his body in tune with his spirit as Djokovic, who meditates and reaches for something more lasting than the solution to a pulled muscle. “I’m doing that every single day, trying to live consciously.”

As for meditation, he said: “I don’t want to tell you what I gain with it but I’ll tell what I lose with it. I lose fear. I lose anxiety. I lose stress. I guess, at the end of the day, that’s what you’re looking for.” Or a winning ace in the final of a slam.

Federer was trouble free in his short match, the 90th win of his many visits to this city. “I’m very happy that I was able to rise to a level that I needed to beat Richard,” he said.

“It was tough. The score shows it, as well. I could have done it maybe a bit faster. At the same time, I was pleased. I think I had some good shots.”