The NIA also said that if he (Rahul) wants to leave the city, he should inform them of his travel plans.
The NIA began quizzing Rahul after it was discovered that he had met alleged Lashkar operative David Coleman Headley, who was arrested by the Federal Bureau of Investigation (FBI) for plotting a major terror attack in India.
According to investigating agencies, Headley had met Rahul during his visit to Mumbai. His name also cropped up in several email conversations with co-accused Tahawwur Rana.
Rahul came into contact with Headley through Vilas who worked at the Moksha gym in the Breach Candy area of south Mumbai, police said.