British tabloid The Daily Mail posted a five-minute clip Tuesday of Zayn Malik smoking and speaking with Louis Tomlinson, who is filming.
Their publicist said: "This matter is in the hands of our lawyers."
In the video, 22-year-old Tomlinson says they are in Peru. The band, on an international tour, stopped in Lima, Peru, last month.
Tomlinson says "joint lit, happy days," and asks his bandmate, "What do you think Zayn about that kind of content?"
"Very controversial," the 21-year-old Malik responds.
The band, which has a clean-cut, wholesome image, emerged from Simon Cowell's British TV series "The X Factor" in 2010 and became one of the world's top-selling groups, with three albums topping U.S. music charts.