The giant mortgage-finance company will likely make the announcement in the next several days, the Wall Street Journal reported Sunday.
Syron would replace Gregory Parseghian, Freddie Mac's current chief executive. Parseghian was named chief executive in June after Freddie Mac ousted longtime chief executive Leland Brendsel because of his failure to rein in accounting abuses.
Numerous accounting problems prompted the company to oust three of its top executives in June and led to the removal of a fourth in August. Several federal investigations are looking into Freddie Mac's accounting practices.
Regulators had demanded Parseghian be removed from his chief executive position in August, but he was allowed to continue while the company searched for a new CEO, the Journal said.