This was disclosed by 50-year-old Headley at a Chicago court during the trial of co-accused Tahawwur Rana (50) in the 26/11 attacks case.
He told jury during the course of questioning on Thursday that Prime Minister Gilani attended the funeral of his father Syed Saleem Gilani and also offered condolences to the bereaved family.
Saleem Gilani, who died in December 2010, was a well-known poet, author and musicologist. He was former Director General of Radio Pakistan and worked for the Pakistani Embassy in Washington DC.
Headley's half-brother Danyal Gilani works as a public relations officer at Prime Minister Gilani's office.