According to RadarOnline.com, the new couple were spotted getting cozy on January 12 at Los Angeles' Chateau Marmont.
A source told the publication that the Hollywood A-listers are "trying their best to keep their relationship a secret to avoid drama with Angie".
Brad and Angelina have reportedly been at each other's throats for over two years as they engage in a nasty divorce war. Their divorce has significantly affected the custody arrangements for their six children.
Only recently has a settlement been reached.
It's no secret that Angelina is no fan of Charlize and it has been reported that the pair have been feuding for years over film roles.
The RadarOnline source also claimed that the two women are butting heads due to their similar philanthropic work.
"Charlize is a Messenger of Peace for the United Nations,” the source explained, adding that United Nations Special Envoy Jolie may have been jealous over her competitor’s role."