The papers said that the charges could be revealed imminently, perhaps even before William Barr, the US attorney general, leaves his post next Wednesday.
The location of the person said to be the subject of the charges, whom The Telegraph is not naming as the identity could not be independently verified, is unknown.
Some 270 people were killed when the US jetliner Pan Am Flight 103 was bombed over Lockerbie, Scotland. Most of those who died were Americans.
Only one person, Abdel Baset al-Megrahi, was convicted over the attack. The Libyan was convicted by Scottish judges in 2001 and sentenced to life in prison.
After being diagnosed with cancer Al-Megrahi was released in 2009 on compassionate grounds, angering the US government and victims' families.
He died in 2012. Mr Barr, currently in his second stint as attorney general, was in the post in 1991 when he announced the charges against Al-Megrahi and a second suspect who was not convicted.
Mr Barr said at that time: "This investigation sends a powerful message. We have the resolve and ability to track down, no matter how long it takes, those responsible for terrorism against Americans."
Monday is the 32nd anniversary of the Lockerbie bombing.
The investigation has drifted for years without major breakthroughs being announced in public.
Robert Mueller, who led the high-profile Russian meddling investigation into the 2016 US election, was in the past involved in the Lockerbie probe as head of the Justice Department's criminal division.
According to The New York Times, Mr Mueller has said that he was haunted by the failure to bring more perpetrators of the attack to justice.
Mr Mueller said in a 2008 speech honouring victims: "We renew our efforts to keep our people safe, and to rid the world of terrorism. We will continue to move forward. But we will never forget."
The Justice Department's press team did not immediately respond when asked to confirm reports that the charges were imminent and the identity of the person involved.