According to EWN, Leshabane will co-own the club with businessman Dr Moeketsi Mosola.
Leshabane is the owner of ABC Motsepe League outfit Mangaung United FC.
Celtic have been in financial trouble for the past few months with players going for months without their salaries.
Tshabalala put the club up for sale in May after he admitted to losing a lot of money from running the club from his pocket.
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