The 65-year-old Australian entertainer, who has undergone a number of operations after falling three metres from a ladder at his Richmond home before Christmas, is expected to be moved from Melbourne's Alfred Hospital to a rehabilitation clinic to continue his recovery.
Meldrum's brother Brian told the Herald Sun: "They are starting to look at the time where he will go into private rehabilitation. They are really happy with his progress and that day is fast approaching. It's a step in the right direction and I am really pleased.''
The star sustained injuries including a fractured skull, brain swelling, a broken collarbone and ribs and a punctured lung in the accident. He was taken off a life support machine on Christmas Day and since then has started speaking slowly.
Although experts have predicted that his recovery will take a "considerable amount of time", his condition has been steadily improving since surgery carried out earlier this month to repair broken vertebrae.
It is believed that Meldrum was in talks with the Seven Network to revive his TV show Countdown shortly before his fall.
Watch Molly Meldrum interview Freddie Mercury on the original version of Countdown below: