The National Investigation Agency team, putting up at a city hotel, is headed by Loknath Behera and comprises two superintendents of police and a special public prosecutor.
However, three days after the team arrived in the US to question Headley, there was no confirmation from American authorities as to when and what kind of access would be granted to the team.
A Federal Bureau of Investigation spokesperson in Chicago told PTI the federal agency would not comment or provide any information on Headley's interrogation.
The US attorney's office spokesperson in Chicago, Randall Samborn, said he "does not have any comment on anything related to David Headley whatsoever".
Repeated calls to Headley's lawyer John Theis seeking comment on the interrogation of his client were not returned.
The 49-year old Pakistani-American has been held at the downtown Metropolitan Correctional Center.
In an indication that access was yet to be granted to the Indian authorities, External Affairs Minister S M Krishna said in his meeting with Secretary of State Hillary Clinton that access to Headley was the "logical next step".
"Access for our authorities to persons who have been apprehended by your government in connection with the Mumbai terror attack is the logical next step," Krishna said in his remarks before the start of the US-India strategic dialogue in Washington on Thursday.
"We are confident that our continued cooperation will lead to realisation of this objective," Krishna added.
Headley had pleaded guilty to conspiring in the 26/11 Mumbai attacks but struck a deal with US authorities in a plea bargain that saved him from the death penalty and extradition to India.
The plea agreement had however said Headley would cooperate with foreign authorities and can be interviewed by them only on US soil.