Amabhubesi were recently rocked by the passing of co-owner Orpheus Panayiotou, who had been financially backing the club since 2009.
As a result the Benoni-based outfit have taken a huge financial hit, with Tovey unable to accept the offer posed to him by the club.
Mlungisi Ngubane has since been appointed TRZ head coach, while recently departed general manager Peter Koutroulis has also been replaced by Thabani Gumede.
Tovey's decision to leave the National First Division outfit could pave the way for an approach from the South African Football Association, who are still to appoint a technical director to new Bafana Bafana coach Gordon Igesund.