Berwick, 66, is a longtime Harvard faculty member and a former health care official with the Obama administration, according to a report on Boston.com.
Appointed by Obama in 2010, Berwick ran the Centers for Medicare & Medicaid Services. However, Berwick resigned in late 2011 after Republicans indicated they would not confirm him, Boston.com reported.
News of Berwick's possible run was first reported this week by State House News Service, according to Boston.com.
Berwick's wife, Ann, is the current chair of the state's Department of Public Utilities.
According to the New England Cable News Twitter feed, Berwick is slated to appear on "Broadside with Jim Braude" tonight at 6 p.m.
State Treasurer and fellow Newton resident Steve Grossman has also said he is strongly considering a run for the corner office. Lt. Gov. Tim Murray has expressed his interest for the governor's seat as well.