The 30-year-old rejoined the Rhinos at the end of last month following his release by Wigan Warriors and was all set to make his second debut against Hull KR.
However, Hardaker has been sidelined since collapsing in the street after suffering a seizure.
He is now edging towards a comeback as Leeds prepare for the first game of the Rohan Smith era this week.
A club statement read: "Leeds Rhinos are pleased to confirm that Zak Hardaker has been given the relevant specialist clearance to return to training and hopes to be available for selection in the near future."
In a further boost for the Rhinos, Liam Sutcliffe (knee), Alex Mellor (sternum), Corey Johnson (knee), Richie Myler (groin), David Fusitu’a (knee) and Tom Holroyd (ankle) are all closing in on returns.
Jack Walker and Harry Newman (both lower limb), meanwhile, are making good progress ahead of an expected return to full training in early June.
Aidan Sezer could be sidelined for another four weeks with his groin injury, while Tom Briscoe is facing up to 12 weeks on the sidelines after undergoing ankle surgery.
Matt Prior and Morgan Gannon will sit out the Salford game through suspension but fellow forwards James Bentley and Zane Tetevano are free to play after completing their bans.