Fifth on the competition's all-time list of top run-scorers, Marsh has already missed the first five matches of the season with a calf injury.
The Renegades have fallen to a 1-4 record in that time, including back-to-back defeats against the ladder-leading Perth Scorchers.
Marsh was initially expected to miss six weeks after suffering the "high-grade" injury to his left calf while running between wickets during a Marsh Sheffield Shield match for Western Australia on November 10.
The 38-year-old has ramped up his training program at home in Perth and is expected to arrive in Melbourne this week.
He is targeting a return to action in January, meaning he will miss at least another two matches in December, and may not play against Sydney Sixers in Coffs Harbour on New Year's Day.
"We'll assess him - he won't play on the 29th, but we'll see if we can take him to Coffs Harbour for the game against the Sixers. We might hold him back until January 3rd, which is the Stars game in Melbourne," Renegades coach David Saker said.
"Our physios haven't had a chance to get their hands on him yet, but he is flying.
"He's doing all his running, he's batting ... I talked to him yesterday and he's confident he'll be back (soon).
"He's a class player and someone who gives us some experience in the middle and the back end of innings."