The former couple are said to have recently shared an "emotional" phone call and are hoping a meeting may repair their relationship.
The Twilight actors recently split following reports of Stewart's affair with director Rupert Sanders.
"They talked on the phone for about an hour, it was very emotional," a source told Look magazine.
"Kristen begged to meet face-to-face so they could talk. It was obvious she was getting through to Rob and he has agreed to see her."
The source alleged that Pattinson feels Stewart deserves another chance following a "moment of stupidity".
"Even though she made a horrendous mistake, Rob can't just switch off his feelings," they said.
"He was madly in love with her and I think believes that it was a moment of stupidity, not a long, drawn-out affair and it would never happen again.
"In Rob's eyes, Kristen was seduced and she's clearly not just sorry but completely destroyed by what she's done."
However, if they were to reunite, Pattinson would reportedly be looking to have more control in their relationship.
"If Rob decides to take her back, he'll have some ground rules. Kristen would have to spend more time in his hometown of London.
"He also would want them to adopt the Angelina Jolie and Brad Pitt way of working - where they take it in turns to do a film so they can be around for time together."
Robert Pattinson was recently reported to be selling the Los Angeles home he owned with Kristen Stewart.