The authorities picked up the two Tuesday in the Nazimabad area in Karachi, Pakistani's largest city and the country's main port, the newspaper reported.
The authorities were looking into their alleged links to Faisal Shahzad, a U.S. citizen of Pakistani origin who was arrested Monday in the failed Times Square car bomb attack.
A Press Trust of India report, quoting sources, said the friend allegedly had made several contacts with Shahzad in recent weeks and had even visited the United States.
No details were available about the detained relative.
The Dawn report quoted sources saying that Shahzad's wife and two children also were in Pakistan, but it was not known if the wife had been detained.
The report said Shahzad is the son of a retired air vice marshal. The father reportedly moved to the port city to take up a senior position with the Pakistan Civil Aviation Authority.
Karachi police officials, however, said they had not received any orders in connection with Faisal Shahzad, Dawn reported.
"We didn't get any order, but at our end we have collected information which confirms that a young man by the name of Faisal Shahzad did arrive in Karachi in April 2009 and left in August the same year. We have received information that some of his relatives live somewhere in North Nazimabad and police are trying to locate the house," a police official told Dawn.
Separately, the report said police in Lahore, Pakistan's second-largest city and capital of Punjab province, had picked up a few more people in the province in the New York incident.
In other developments, Pakistani Interior Minister Rehman Malik said there had been no request from the United States for information relating to Shahzad, the state-run Associated Press of Pakistan reported.
"Until and unless we are not provided proper information trough proper channel, I cannot verify the involvement of any Pakistani citizen in the New York attack plot," he told reporters while assuring Pakistan would extend full cooperation when any request is received from the United States.
"Let me reiterate the strong resolve of Pakistan that no one would be allowed to use Pakistani soil for terrorism in any part of the world," he said.