Martin has rented the mansion of Los Angeles Lakers general manager Mitch Kupchak, who has a 4,000-square-foot place off Old Montauk Highway, while Paltrow's home is just a few blocks and a short walk away, reported the New York Post.
"Chris can often be seen strolling or jogging around the area on his own, or surfing in Montauk with his and Gwyneth's kids Apple, 10, and Moses, 8," a neighbour said.
Despite the separate addresses, they were spotted together many a times.
The couple announced their split in March after 10 years of marriage.