Keith Moss, who was the consul-general in Paris at the time of the princess' fatal car crash in 1997, said the comment came from a French man who he believed was associated with the country's diplomatic protection service. Moss could not recall the man's name or title.
Moss said the man approached him in an area of the Pitie-Salpetriere hospital where dignitaries including the French president had gathered after the crash.
"At some point in the conversation he asked me whether we knew that the Princess of Wales was in France, and if we did know, why his services had not been informed," Moss testified at the British inquest into the death of Diana and her boyfriend, Dodi Fayed.
Had they known, the man added, the French could have "conducted discreet surveillance of security coverage."
Moss was asked at the inquest whether the official had suggested that if this had been done, the princess might not have been killed. "That was the inference," he said.
Fayed's father, Mohamed Al Fayed, has alleged that British agents working at the embassy knew about the visit and were part of a plot against the couple directed by Prince Philip.
Moss said he and then British Ambassador Michael Jay had not known Diana was in Paris at the end of August 1997.
Moss was closely involved in arrangements to return Diana's body to Britain, and consulted with the embalmers who prepared her body.
Al Fayed has alleged that the embalming was intended to cover up evidence that Diana was pregnant with Fayed's child.
Moss said the embalmer, Jean Manceau, had recommended the procedure to make the body presentable for family members and dignitaries coming to pay respects, and to prevent deterioration in a warm room.
Al Fayed has alleged that embalming Diana in France was illegal; it was done on instruction from British intelligence agency MI6; and MI6's instructions were conveyed to the ambassador, who communicated them to Maud Morel Coujard, who was a deputy public prosecutor in Paris in 1997.
Coujard testified Tuesday that she had no involvement in the decision.
Manceau told the inquest that it was his idea to embalm the body, and he was not acting under orders.
Moss said he believed that there was nothing unusual about the decision.
Michael Mansfield, a lawyer for Al Fayed, questioned why Moss had not made an effort to note the name of the official who approached him, and why Moss had not mentioned the incident to any other official until 2004, when he made a statement to London police.
"You do now recognize, don't you, that it might have been quite significant to discover ... who this man was, and how he thought he would have been able, if they had been tipped off even informally, and mounted a discreet surveillance operation, how they thought they might have prevented the death of the Princess of Wales," Mansfield asked.
Moss said he did not think it was significant at the time, later adding that it was one of many conversations he had had with various people during a stressful day.
Responding to other questions from Mansfield, Moss said he was aware that the British security services had a post in the Britain's Embassy in Paris, but he did not know whether it involved MI6, or British domestic spy agency MI5 or both, and he did not know who the agents were.
Mansfield suggested one name - Richard Spearman, who was listed as the first secretary in the political section.
Spearman was "posted to Paris a few days before the crash. Did you know that?" Mansfield asked.
Moss said he did not.
Richard Tomlinson, an MI6 officer from 1991 to 1995, has claimed that Spearman was one of two intelligence agents in Paris at the time. Al Fayed has suggested that Spearman may have been involved in engineering a murder plot, though perhaps he was not directly involved.
The inquest - required by British law when someone dies unexpectedly, violently or of unknown causes - began earlier this year and had been delayed for 10 years because of two exhaustive investigations by French and British police.