Leaner became a free agent after Sekhukhune United failed to exercise the option to extend his contract before the required deadline, allowing the 28-year-old to leave the club without a transfer fee.
The public broadcaster established that Chiefs have now tabled a firm offer to the Bafana Bafana goalkeeper, with only the final formalities, including personal terms and a medical, still to be concluded before the move is completed.
The latest development marks a significant turnaround in the race for Leaner, who had attracted strong interest from both Pirates and AmaZulu following confirmation of his departure from Sekhukhune.
Reports elsewhere have indicated that Pirates have since ended their pursuit, leaving Chiefs in pole position to secure one of the country's most sought-after goalkeepers.
Should the deal be finalised as expected, Leaner will strengthen AmaKhosi's goalkeeping department ahead of the new season, joining captain Brandon Petersen, Bruce Bvuma, and Fiacre Ntwari as new coach Fernado da Cruz looks to increase competition for the number one jersey.
Leaner impressed during his spell at Sekhukhune with then coach Eric Tinkler restoring him to be first choice last season – and the keeper earned recognition at international level with the national team, making him one of the standout shot stoppers available during the current transfer window.
Barring any late complications, the former Sekhukhune player is expected to complete his move to Naturena in the coming days.