Mohamed Al Fayed has been asked for evidence showing that his son Dodi and Princess Diana were murdered in a plot involving the Royal Family.
Baroness Butler-Sloss, who will hear inquests into the deaths, is deciding whether Prince Charles and Prince Philip will be called as witnesses.
She said she had not been given "a shred of evidence" about the claims.
She has been asked by lawyers for Mr Al Fayed to postpone the inquests for six months to ensure adequate preparations.
The princess and Dodi Al Fayed died in 1997 in a road crash in Paris.
Their inquests are currently scheduled to start in May.
Harrods boss Mohamed Al Fayed won a High Court ruling on Friday that the inquests should be heard before a jury.
The decision overturned a ruling by deputy royal coroner Lady Butler-Sloss that she would sit alone.
Mr Al Fayed wants Prince Charles and Prince Philip to give evidence.
He maintains Diana and his son were murdered and claims their deaths were part of a secret plot by the British establishment.
At a pre-inquest hearing on Monday, Lady Butler-Sloss told Mr Al Fayed's legal team she would need evidence if she were to present the allegations to the inquest jury.
Michael Mansfield QC, representing Mr Al Fayed, told her she had the evidence already as Mr Al Fayed had given it to the inquiry into the case conducted by former Met Police chief Lord Stevens.
He told the court: "A starting point which will undoubtedly come to light during the inquest is Princess Diana's premonitions or fears."
He added: "Mohamed Al Fayed gave a statement to the police about this and what he had been told by Princess Diana during the summer months, about her concerns, her fears and so on.
"He has already provided that."
Mr Mansfield said both the Prince of Wales and the Duke of Edinburgh were "witnesses of relevance".
He said Mr Al Fayed had only been provided with "a summary" of an interview Prince Charles had given investigators.
Prince Philip "was responsible for letters sent to Princess Diana" but has refused to be interviewed and Mr Al Fayed should be told the reasons why, he said.
Mr Mansfield also said he would want to see the original copy of a letter allegedly written by Princess Diana to her former butler Paul Burrell.
Earlier he asked for the inquests to be put back for six months saying expert witnesses had a "massive amount of work" to do before they could give evidence.
But Lady Butler-Sloss told the court she felt a delay would be "very hard on the families".
The princess and Mr Al Fayed had been pursued by photographers on 31 August when their Mercedes crashed in the Pont d'Alma tunnel in Paris.
The Stevens inquiry concluded that Diana had died in a tragic accident and there had been no conspiracy and no cover-up.