Sources said the pair were "very affectionate" during the search, reported the New York Post.
Shayk, 30, has been living at 166 Perry St in a 2,462-square-foot loft, but she put the house on the market for USD 3.99 million in December.
Her luxurious pad has 12-foot ceilings, wide-plank oak-wood floors and floor-to-ceiling windows. It also has a gym and "roof solarium."
Sources said she needs more space, perhaps for 41-year-old Cooper. Listing broker, Douglas Elliman's Jacky Teplitzky, declined to comment on the report.
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