A formal announcement will be made later today.
The key question, and one in the gift of the Queen, is whether the Princess should be granted a full state funeral, normally reserved for the monarch or, as in the case of Winston Churchill in January 1965, commoners who, through exceptional service to the state, are deemed to have earned the privilege.
The discussions are being handled by the head of the Queen's Household, Lord Airley, who was at RAF Northolt, Middlesex, last night for the return of the Princess's body.
He will be consulting the Queen and the Prince of Wales, the family of the Princess, royal advisers and Downing Street.
It is likely that public opinion, which may be in favour of a full state ceremony, will also be taken into account.
A spokeswoman at Buckingham Palace said last night: "The final details are being finalised and there will be an announcement tomorrow."
On 30 January 1965 the body of Sir Winston, the last commoner to be given the accolade of a state funeral, was taken to St Paul's Cathedral in a naval gun carriage.
It was first used for Queen Victoria's funeral, and subsequently for Edward VII, George V and George VI.
Sir Winston's body had lain in state in Westminster Hall for three days and both Houses of Parliament were adjourned for a week.