Meldrum's manager Mark Klemens says doctors are happy with Molly's progress since his fall two weeks ago landed him in hospital with a fractured skull.
"He's likely to be in intensive care potentially for another week," Mr Klemens told AAP on Saturday.
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"There's a chance he could be out of intensive care and into a ward by the end of next week," he said.
Mr Klemens said the TV personality and industry stalwart was suffering some discomfort as his broken collarbone and ribs continued to heal.
Molly also suffered a fractured skull and underwent surgery to relieve swelling on his brain after the fall at his home on December 15.
He was breathing without a ventilator but was yet to engage in any conversation, bar a few mumbled words, Mr Klemens said.
"But the doctors are happy with the progress. This is the expectation with those sorts of injuries."
Molly's brother Brian and long-term personal assistant Yael Cohn are still the only two people to have contact with the star, to avoid overstimulation, Mr Klemens said.
Meldrum, 65, suffered the injuries after falling three metres down stairs near the spa at his Richmond home while he was putting up Christmas decorations.
He was put under heavy sedation and on a ventilator, and later underwent several operations to repair fractures to his collarbone and ribs.
