Ms Bishop says she won't reveal the man's identity but the government is working with British authorities who are providing consular assistance to his family.
It comes shortly after the vice chairman of EgyptAir withdrew a claim by the airline-- that debris found floating in the Mediterranean Sea was from the missing plane.
Egypt Air Flight MS 804 was just 20 minutes from landing at Cairo International airport when authorities say it vanished without warning.
Since then, distressed relatives of those on board have been ushered into a closed-off area of the airport to wait for news.
But those who emerge say they haven't been given any new information.
Father Arsinous is an Orthodox priest whose brother was on board the flight.
"We just found out from the media that they found the wreckage of the aeroplane on the Greek side. I hope they find anyone who we can pray over."
EgyptAir had released a statement claiming the Egyptian Foreign Affairs Ministry had declared wreckage from the missing aircraft had been found near the Greek island of Karpathos.
Greek authorities refuted the claims, saying they had found a piece of wood, and some materials that don't come from a plane.
EgyptAir Vice Chairman Ahmed Adel has since retracted the statement and says the search and rescue effort is still ongoing.
In Paris, where the flight had departed, more passenger relatives have been boarding flights to Cairo.
Stephane Gicquel,from the National Accident Victims' Federation, says they face a difficult wait until a clearer picture of what happened emerges.
"What people need to understand is today there is still something very surreal. No one has looked these families in the eye to say this plane crashed and that their loved ones are dead. So it's important to understand that these families are still going through a waiting period for information, and that's why it's important for them to be reunited, for the government, for the French president, the prime minister. That was their decision."
Officials say calls from air traffic control to the plane had gone unanswered just before it left Greek airspace.
Greece's defence minister, Panos Kammenos, describes the airbus making "sudden swerves" before disappearing from radar screens.
"At 3:37 the plane, which was 10 to 15 miles inside Egyptian airspace at 37 thousand feet, made a 90 degree turn to the left, and then a 360 degree turn to the right. It descended from 37,000 feet to 15,000 feet. The picture we had was lost at 10,000 feet."
Egypt's aviation minister, Sherif Fathi, says a terrorist attack is a more likely explanation than a technical failure.
"I don't want to go to speculations, and I don't want to go to assumptions, like others, but if you analyse the situation properly, the possibility of having a different action or having a terror attack, is higher than the possibility of having a technical (failure)."
United States officials say a review of satellite imagery has shown no signs of an explosion aboard the flight.
They've also cautioned against media reports suggesting Washington believes a bomb was responsible.
White House spokesman Josh Earnest says the U-S isn't ruling out any possibilities.
"Let me start by offering our thoughts and prayers to the families of those who were aboard EgyptAir flight 804. It's too early to definitively say what may have caused this disaster. The investigation is underway and investigators will consider all of the potential factors that could have contributed to the crash."
Egyptian President Abdel Fattah al-Sisi has since ordered his country's civil aviation ministry and armed forces to take all necessary measures to locate the wreckage.
