Andy Murray (right) played a singles and a doubles match at the charity event in Glasgow

Britain's Andy Murray hopes to make his competitive return in Brisbane in January following a hip injury - but only if he is 100% fit.

The Scot lost 6-3 3-6 10-6 to world number two Roger Federer as part of a charity event in Glasgow on Tuesday.

It was the first time Murray, 30, had played in public since he lost to Sam Querrey at Wimbledon in July.

"I am in a significantly better place than at the end of Wimbledon and in the build-up to the US Open," said Murray.

"Walking was a big problem for me [at that time]," he told BBC Sport.

Murray, who slipped to 16th in the latest world rankings, said he was confident of getting back to full fitness, but admitted that it could take time for him to find his best form.

He will travel to Miami later in the year for his regular off-season training block and "hopes" to return to competition at the Brisbane International in January.

The tournament is held two weeks before the Australian Open, the first Grand Slam of 2018, which gets under way on 15 January.

"When I get back on the court again my best form might not come immediately but there's nothing that's making me think I can't find it," Murray added.

"I'll come back when I'm ready and 100% fit. I believe I will get back to that."

Murray also played a doubles match with brother Jamie against Tim Henman and Mansour Bahrami during Tuesday's 'Andy Murray Live' external-link event in Glasgow.

Analysis

BBC tennis correspondent Russell Fuller in Glasgow

Eight weeks before his hoped for return in Brisbane, Murray put down an encouraging marker as he was beaten 10-6 in a deciding tie-break in Glasgow.

There was time for Federer to hold serve in a kilt early in the second set (he was told to 'Get yer kilt back on' when he lost the first few points after dispensing with it), but there were also plenty of competitive rallies.

Federer - on his first visit to Scotland - played in a kilt at one stage

We are getting used to seeing Murray walk with a slight limp but for the most part he ran and moved well. He covered a lot of ground in rallies which frequently switched direction, and struck the ball soundly.

His serve is not yet back up to full speed, but that is only to be expected of someone rehabbing a serious hip problem.

Next to Miami, where two weeks of pre-season training will give him a clearer picture of whether he will be celebrating the New Year in Australia.

US Open bid 'a mistake'

Murray endured a frustrating 2017 season in terms of both form and fitness. He was knocked out of the Australian Open in the fourth round and went on to miss a month with an elbow injury.

He fared better at the French Open, reaching the semi-finals, but lost in the first round at Queen's Club before visibly struggling with the hip as his Wimbledon title defence was ended by Querrey in the quarter-finals.

Still ranked number one, Murray travelled to New York for the US Open but pulled out two days before the tournament began having failed to recover sufficiently.

"I made, probably, a bit of a mistake trying to get ready for the US Open but it was the last major of the year," said Murray.

"I've been training for a few weeks now. Some days I've felt great, some days I've felt not so good, but I'm getting there."

Federer, who missed the latter half of the 2016 season with a knee injury before winning the Australian Open and Wimbledon this year, said it was "wise and worthwhile" to take time to recover.

"When you come back, you want to be at 100%. Otherwise you feel like you can't beat the best and can't win the major tournaments," said the 36-year-old Swiss.

"I'm sure Andy has a lot of years left. You need to have goals but sometimes they need to be postponed."

Emotional Murray withdraws from US Open

'I miss playing tennis'

Murray said his "goals have changed" after the second lengthy injury break of his career, following back surgery in 2013 that kept him out for several months.

"I just want to play tennis again. It's my life and my job, and that's my goal just now," he said.

Murray became world number one for the first time at the end of 2016 but having not played since July, he has now dropped out of the top 10 for the first time since October 2014.

"Last year, I played a lot of tennis, especially at the end of the year. My goals have changed now," he said.

"When you're fit and healthy, you want to win every tournament and get to number one in the world. When you're not playing, it's like, I miss playing tennis.

"I just love to be back on a match court and competing again."