The pair are said to be eager to escape the spotlight and want to move to Cornwall after falling in love with the area on a recent trip, reported Showbizspy.
"When Robert was growing up the whole family would go on idyllic holidays to Falmouth, Truro and Newquay so he is always thought of the area fondly," a source said. "A few weeks ago, he took Kristen for a four-day trip and hardly anyone bothered them.
They had a fabulous few days just being normal. They agreed to buy a bolthole there and, after setting their hearts on a couple of remote cottages, are hoping to finalise on one soon," the source added.