AceShowbiz - Amid his divorce, Jeff Bezos and Lauren Sanchez are about to take a bigger step in their relationship. The lovebirds are said to be planning to stop hiding their romance and live together.

"They are very much together," says a source to PEOPLE. In addition, the source claims that the 55-year-old billionaire and his rumored former news anchor girlfriend "are planning to move in together."

The Amazon CEO and Sanchez allegedly felt "a sense of relief" now that their affair has become public consumption, because at least, they don't have to hide it anymore. Another source previously shared, "The circumstances of their relationship aren't exactly ideal, but they're two adults who are very much in love," noting that the secrecy around their relationship has "been a dark cloud hanging over them."

It was also said that the fact that their affair went public didn't affect them to the slightest. Instead, it only makes their relationship go stronger than ever. "The world is catching up to it, but it has had zero impact on their relationship," said a source who claims to be close to the pair. "They've never been stronger."

News of Bezos' cheating allegations first hit the internet soon after the businessman announced divorce from wife of 25 years, Mackenzie. A purported texts between the pair were recently leaked online, showing how he declared his love for Sanchez and even went as far as sending the former news anchor a slew of lewd pics of himself. He reportedly sent Sanchez a close-up picture of his penis that "is too explicit to describe in details."

Meanwhile, the 49-year-old has yet to address the status of her marriage to Hollywood mega agent Patrick Whitesell.