A French source has told AFP that search teams have located the box to within 10 metres (yards).
Earlier, the head of the Egyptian investigating commission, Captain Shaker Qallada, was quoted as telling the state MENA news agency that they hoped to have the black box by Saturday.
"The French teams have found the location of one of the two black boxes and are trying to recover it," he said.
"If the recovery operation is successful, the black box will be turned over to Egyptian authorities on Saturday morning," he said.
Another source close to the search said the black box was already being brought up to the surface by the Scorpio robot of France Telecom Marine when the recovery operation had to be delayed to allow the presence of Egyptian officials.
The source said the box dubbed Black Box South had been found in 1000 metres of water 1300 metres south of what was believed to be the signal from the other black box.
The Flash Airlines Boeing 737 crashed shortly after take-off for Paris from this Red Sea resort, killing 134 French tourists and a Moroccan as well as 13 Egyptian crew members.
The black boxes are expected to reveal the exact cause of the tragedy, which Egyptian and French experts believe was the result of a technical fault or other accident and not terrorism.
The French experts had previously said the two black boxes were believed to have plunged to a depth of up to 800 metres (2600 feet) and spread 1.5 kilometres (5000 feet) apart.
One black box records the movements of the plane's controls and the other the voices of the pilot and co-pilot. It was not immediately known which of the two has been located.