Buckingham Palace has been sent a copy of the book by Princess Diana's former butler Paul Burrell, so it can consider the legal implications.
Diana was killed in a car crash in Paris in 1997
Extracts of the book have been published this week in the Daily Mirror, including alleged letters from Prince Philip to Princess Diana.
It is understood that officials at Buckingham Palace have spoken with their legal advisers to see if the law of copyright has been breached.
The palace would view the correspondence as private as they were not bequeathed to Mr Burrell.
The latest extract from his book focused on letters allegedly from Prince Philip to Princess Diana.
They were allegedly written in 1992 at the time Diana's marriage to Prince Charles was disintegrating.
The Daily Mirror reported that the Duke of Edinburgh had told the princess: "I cannot imagine anyone in their right mind leaving you for Camilla."
The Mirror said Prince Philip told Diana: "We do not approve of either of you having lovers. Charles was silly to risk everything with Camilla for a man in his position.
No public inquiry
"We never dreamed he might feel like leaving you for her. Such a prospect never even entered our heads."
Earlier on Tuesday, Downing Street confirmed there would be no public inquiry into Princess Diana's death.
Diana and Dodi Al Fayed died early on the morning of 31 August, 1997 after the Mercedes they were travelling in crashed in the Pont D'Alma tunnel.
The prime minister's official spokesman rejected calls for an inquiry into the crash.
Mr Burrell alleged in Monday's Daily Mirror that the princess had feared her life was in danger 10 months before her death.
But the prime minister's spokesman said: "Everybody knows there has been an exhaustive investigation by the French authorities into the circumstances surrounding Diana's death.
"There will be nothing to be gained from repeating that here.
"But clearly there will be a routine coroner's inquest in Britain once the French legal processes are completed."
The princess is reported to have written in a letter to Mr Burrell that she feared the brakes of her car were going to be tampered with.
Mohamed Al Fayed, whose son Dodi - Diana's lover - also died in the Paris crash, has since urged Tony Blair to launch a full inquiry into her death.
The princess reportedly wrote to Mr Burrell: "This phase in my life is the most dangerous."
She allegedly named someone who was "planning an accident in my car, brake failure and serious head injury".
In the letter - reportedly written a couple of months after her divorce from Prince Charles was finalised in October 1996 - Diana believed the plot had been hatched "in order to make the path clear for Charles to marry".
Mr Al Fayed, who owns the London store Harrods, said publication of Diana's alleged letter confirmed the suspicions he had often voiced and which had "so far been ignored".
"The prime minister must now accept that the time is right for a full public inquiry," he said.
"Further delay will look as though he is colluding in a cover-up and the people of this country will not tolerate that."
Mr Al Fayed has repeatedly claimed Diana and his son were murdered by British secret services because their relationship was embarrassing to the royal household.
The French inquiry in 1999 blamed French chauffeur Henri Paul, concluding he had taken a cocktail of drink and drugs and had been driving too fast.
In August, Surrey Coroner Michael Burgess announced he would conduct inquests into the death of Diana and Mr Al Fayed, but did not specify a date.