The PSNI has said that detectives from its Serious Crime Branch have initiated steps to obtain all the material from the Belfast project at Boston College.
It said that this was in line with the PSNI's statutory duty to investigate fully all matters of serious crime, including murder.
Dozens of former paramilitaries, both loyalist and republican, gave accounts of their involvement in the Troubles on the understanding their interviews would not be made public until after their deaths.
The PSNI already obtained a number of the tapes through the courts in the US.
US news network NBC is also trying to secure access to the archive on the grounds of public interest.
Amid uncertainty about the status of the tapes still held in the archive, Boston College had offered to return the material to those individuals who have given interviews.
Some of the interviewees have threatened to sue the college over its handling of the issue.