Stakeknife has been named by the media as Belfast man Freddie Scappaticci, who denies claims he was the Army's most high ranking agent in the IRA.
The Chief Constable told Stormont's justice committee that the secretary of state and the Department of Justice had said there would be no more money.
The investigation could cost Â£35m.
It is expected to take at least five years, at an estimated cost of Â£7m per year.
The Police Service of Northern Ireland (PSNI) Chief Constable George Hamilton has previously said he wants to bring in a team of detectives from outside Northern Ireland to conduct the inquiry.
On Thursday, he told the justice committee that the PSNI will have to fund the work from within its existing budget.
No additional money will be available to police to investigate the alleged activities of the Army agent codenamed Stakeknife, MLAs have heard.