The Ugandan FA gave the Scottish Premier League side permission to speak to the Hungarian just 24 hours after caretaker-manager Stephen Frail was dismissed.
A Hearts statement read: "Heart of Midlothian Football Club confirmed today that the club was in talks with Laszlo Csaba regarding the vacant managerial position at Tynecastle. Csaba was granted permission to speak with the club by the Ugandan Football Association as the Romanian-born coach is currently Ugandan national team manager."
Rogers Mulindwa, the Ugandan FA's media officer, admitted Csaba is expected to leave his current post. "The search for a likely replacement has already started in the background," he told The Scotsman newspaper.
"We would have liked him to stay, but all indications are that he is leaving. We have already drafted an advert for the job. We cannot sit back and have our arms crossed until Csaba acts. We have to start looking now."