According to reports, Headley had stayed on the fifth floor of 'A Block' of Shyam Niwas housing society in south Mumbai's Breach Candy area.
Speaking to a leading daily, 75-year-old Mrs Kriplani said, "David Headley was a very sweet and charming man... He was extremely courteous, and never created any trouble for us."
According to Mrs Kriplani, Headley used to stay in the apartment for nearly a week and then he used to go travelling on work for two to three months.
Headley had told the elderly couple that he was running an immigration agency in the city.
Meanwhile, sources said that the National Investigation Agency (NIA) is investigating Headley's possible role in the Delhi, Ahmedabad and Bangalore serial blasts.