Glasgow: Come Tuesday, Andy Murray will walk out to play competitive tennis for the first time in 118 days. After his limping exit from the Wimbledon quarter-finals, followed by an aborted attempt to appear in August’s US Open, this is the longest period he has spent away from a match court in his entire career.

Rather than an official ATP tournament, we are talking about a fund-raising exhibition entitled Andy Murray Live. Such extra-curricular outings are usually ignored by the wider game, yet Tuesday’s outing will be assessed as closely as many finals — and not just because his opponent is Roger Federer. Everyone wants to know how Murray’s dodgy hip is bearing up.

It is less than a month since Murray began hitting balls again, mostly in the All England Club’s off-site facility at Raynes Park, south Wimbledon.

Happily, though, the news from insiders has turned increasingly upbeat in the past week or two. The official plan of returning to the ATP Tour in Brisbane, in a tournament that begins on New Year’s Eve, is starting to look like more than just a pipe dream.

The key factor in Murray’s rehabilitation has been the system of movement called “gyrotonic” — a cross between pilates and yoga that uses pulleys and weights to spin the body through a series of low-impact contortions. He has flown in his American instructor, Teresina Goheen, to work with him on a daily basis. And the improvements have been encouraging enough for both Murray and his coach Jamie Delgado to post videos of his tennis practices on social media — always a sign of optimism in the camp.

Tuesday’s match will represent an important staging post in this journey. It is possible for players at this level to stage an entertaining exhibition without really exerting themselves; Murray himself did this when he visited Zurich in April to play Federer in the Match for Africa 3, even though he was off the tour at that point because of a damaged elbow tendon.

Yet, the word is that he wants a more rigorous test this week, to give himself a barometer of how close he might be to tournament readiness.

“We’re going to have a good time,” said Federer last week, “and I think it’s wonderful what he [Murray] is doing in his philanthropic efforts.

“When people came away from Zurich, so many told me how much fun Andy actually was, what a great sport he was, so I was so happy he did that, and I can’t wait to return the favour. Going to new places is something I always really enjoy, so I’m excited to be going to Scotland for the first time.”

As the finest tennis player Britain has produced, Murray stands at the centre of a mini-industry, involving sponsors, agents, manufacturers and so on. Yet the true state of his health remains opaque to everyone. Even Murray himself does not know how his body will respond to competition, let alone the stress of daily combat on hard surfaces in the 40C heat of Australia.

“Tennis is a difficult sport for coming back from injuries,” says Michael Davison, a sports medicine specialist and managing director of Isokinetic London. “You can’t manage your minutes, like you would in football by coming on for half an hour towards the end. No one knows how long a match will last or how far you might go in a tournament. So an exhibition like this is the nearest thing Murray will be able to get to playing competitive tennis in a controlled environment.”

At least Murray still believes he can do without an arthroscopy, which would probably put him out for six months without offering any guarantee of resolution.

Still, Davison suggests that Murray’s progress to date sounds promising. “Murray’s people talk about rest and rehabilitation but it’s not as if he isn’t training hard,” he said. “Joints do wear out, but Andy is still relatively young. He won’t opt for surgery unless it really is the final option.”