Stewart, 23, and Pattinson, 27, who parted ways earlier this year, have reportedly been meeting secretly since sometime, reported Hollywood Life.
"Kristen doesn't want to keep her relationship with Rob a secret anymore. She doesn't want to have to sneak around whenever she sees Rob - it makes her feel like she's doing something wrong and she's not," a source said.
"Kristen wants to go public with her relationship with Rob. She wants to go to concerts and other places with him, like they used to. Rob is being a lot more cautious and isn't ready to have everyone know his business when it comes to who he's dating," the source added.
The couple tried to patch up after a brief split but finally decided to call it quits in May.