Murray has been troubled with a hip injury, which has kept him off the court since Wimbledon.
The Briton, who enjoyed being world number one just 12 months ago, has fallen out of the top 10 to number 16 in the rankings.
"I hope I'm there," The Independent quoted Murray, as saying about his plan to return at the Brisbane International, which starts on December 31.
"Things have been going pretty well so far in the rehab. But you just never know. You take each week as it comes. You have setbacks and then things come on quite quickly as well," he said.
Speaking before playing a charity exhibition match against Roger Federer in Glasgow, Murray said, "I've been training for a few weeks now. Some days I've felt great, some days not so good, but I'm getting there. I'll come back when I'm ready and 100 per cent fit."
Murray, who started the year as world No 1 but fell this week to No 16 in the rankings, had not played a match in public since he limped to defeat by Sam Querrey in the Wimbledon quarter-finals. He had hoped to return at the US Open at the end of August but pulled out less than 48 hours before it was due to start.
Earlier, he made an aborted attempt to return in US open, but the injury prevented him from doing so.
Murray, 30, suffered defeat at the hands of Sam Querrey, as he played through the pain caused due to the chronic injury that had plagued him since the French Open in June, earlier this year. (ANI)