Amazon CEO , Jeff Bezos and Lauren Sanchez are still going strong now that their relationship is public.

“They are very much together, and are planning to move in together,” a source tells PEOPLE.

News of the world’s richest man’s romance with the news anchor and helicopter pilot, 49, first broke in early January after Bezos, 55, announced his divorce from wife MacKenzie after 25 years together in a joint statement on Twitter.

Their split is likely to be one of the most expensive ever — since Bezos is the richest man in the world worth an estimated $137 billion.

While Sanchez and Bezos have not been spotted out together since news of their relationship broke, a source told PEOPLE in last week’s issue the new couple is “in constant contact.”

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