A bid has been submitted but Cerberus is undecided about how it would structure the acquisition, the Journal said.
Still up in the air is whether Cerberus will buy the 200-store grocery chain outright or leave some of the company in the public domain, the source said.
In May, Harris Teeter said it was involved in negotiations with "certain parties, about different possibilities for the company's future.
Cerberus, which usually goes after companies that are in distress, may be pursuing Harris Teeter to complement its other grocery store holdings, several of which were purchased this year from Supervalu Inc., the report said.
2014: The Year in Music [PHOTOS]