The experienced left-hander, who hit a fighting hundred to help Australia scramble to a draw in the first Test against Pakistan last month, has been out of action since the second Test of that series.
His stability at the top of the order — which is already without the banned Steve Smith and David Warner — has been sorely missed after a string of recent Australian batting capitulations.
He underwent surgery late last month and is already back running.
“I m 10 kilograms lighter than I was in South Africa maybe seven months ago, so I m sure that helps the knees in some respects,” he told cricket.com.au.
“My recovery is going really well so far. I m trying to keep it cool, but it s actually going really well.
“I feel like I m a little bit ahead of where I should be,” added the 31-year-old.
“If I keep doing the little things right — looking after my body, being disciplined — hopefully that ll transition to me coming back in time.”
Cricket Australia s website said there was a chance Khawaja could play in Queensland s Sheffield Shield match against Victoria starting on November 27.