The MI6 officer seized during the secret mission in Libya at the weekend was carrying a note signed by David Cameron.
The Prime Minister wanted the note hand-delivered to the rebel leaders to help help win their trust in the campaign to oust Libyan leader Col Muammar Gaddafi, according to the Daily Mirror.
In doing so he was following in the footsteps of Baroness Thatcher, who liked to begin "difficult negotiations" with personal messages while she was Prime Minister.
The Foreign and Commonwealth said it was investigating the report on Tuesday morning.
The claim came after William Hague told the House of Commons on Monday that the Prime Minister was aware that SAS soldiers and MI6 officers were to mount the secret mission in Libya.
The Foreign Secretary made clear the Prime Minister knew about last week's operation, which ended in embarrassing failure when the British personnel were held captive by Libyan opposition groups.
As the secret mission was condemned in the Commons as "ill-conceived, poorly planned and embarrassingly executed", a Whitehall blame-game broke out over the operation.
Guarded by Special Forces troops, British intelligence officers last week arrived near Benghazi by helicopter as a "pathfinder" exercise to prepare the ground for a larger diplomatic delegation.
The secret mission failed when local Libyan forces put the British personnel in "temporary detention". Drawing laughter from MPs, Mr Hague said that was caused by a "serious misunderstanding" about their mission.
The Prime Minister has faced persistent criticism over his handling of the Libyan crisis, and Labour said the botched "diplomatic mission" has raised fresh questions about the Government's competence.
Speaking about the signed letter, one senior Special Forces source told the Daily Mirror: “David Cameron ... (was) trying to do a Maggie Thatcher and using the SAS regiment as his own tame fighting force.
“Throughout this flawed mission and the fallout from it, it has been clear the SAS men were not backed up – even when they were rescuing civilians in the desert.”
On Monday morning, Downing Street said that Mr Hague was responsible for the mission in the Benghazi area.
No 10s version of events caused anger in the FCO, where diplomats saw it as an attempt to shift blame. "Some of the Foreign Secretary's colleagues are keen to blame him for just about everything these days," said one source.
Mr Hague later told MPs that Mr Cameron and other ministers were privy to the secret operation.
He added: "The Prime Minister and other colleagues were aware that we would attempt to put a diplomatic team into eastern Libya."
The Foreign Secretary said he took final responsibility for the mission but insisted that the "timing and details" were down to military commanders and Whitehall officials.
Some critics have questioned the decision for the officials to travel by helicopter in the early hours of Friday morning, instead of making the short journey from central Benghazi in the open.
Mr Hague said: "The timing and details of that are operational matters decided by the professionals, but ministers must have confidence in their judgments as I do and must take full ministerial responsibility for their judgments and decisions, as I do."
Sir Menzies Campbell, the former Liberal Democrat leader, told Mr Hague the failed mission had damaged Britain's international standing.
"I regret what I am about to say. Isn't it clear that this mission was ill-conceived, poorly planned and embarrassingly executed," he asked. "What is he going to do to restore the reputation of the United Kingdom in relation to foreign policy in the Middle East?"
Douglas Alexander, the Labour shadow foreign secretary, said the failure of the mission was "just the latest setback for the United Kingdom and raises further serious questions about ministers' grip and response to the unfolding events in Libya."
Mr Hague said it was right to try to make contact with the Libyan opposition, saying he intended to "send further diplomats to eastern Libya in due course". However, he said those officials will be deployed "on a different basis".
He also rejected calls for Britain to arm the Libyan opposition, pointing to the United Nations arms embargo. Mr Cameron last week told MPs he was willing to consider military aid to the rebels.