Federal prosecutors have been looking into whether Gov. Andrew M. Cuomo’s administration granted special access to rapid coronavirus test results for the governor’s family and other influential people, according to two people with knowledge of the discussions. Investigators from the Eastern District of New York had been looking into the handling of data on nursing home deaths by Mr. Cuomo’s office. More recently, their focus expanded, according to the people, to include questions surrounding a priority testing program that benefited Mr. Cuomo’s close family members, including his brother, Chris Cuomo, in the early weeks of the pandemic. Those who received special access to testing and fast results during that period also included Giorgio DeRosa, a top Albany lobbyist and the father of the governor’s most senior aide, Melissa DeRosa, according to two people with knowledge of the tests who spoke to The New York Times.