Years later she had three children with Marc Antony, then a key Roman political and military leader.
Their ill-fated love affair has been the subject of countless artworks, including paintings, movies, an opera, and a Shakespeare play.
One theory is that Taposiris Magna may have been chosen as the couple's burial site because of its temples to the Egyptian god Osiris and his wife, Isis.
"We hope Cleopatra's tomb is located in this site," Hawass said. "This could be an important discovery—bigger than that of King Tutankhamun's tomb."
(Related: Get the facts about the curse of King Tut's tomb.)
John Baines is an Egyptologist at Oxford University's Oriental Institute who was not involved in the excavation.
"Aphrodite is not associated with indigenous Egyptian temples, so her presence may suggest a non-Egyptian, perhaps Ptolemaic connection," Baines said.
And masks similar to the one Hawass thinks might have belonged to Marc Antony were "normally part of a burial and are relatively common objects from Greco-Roman Egypt," he added.
Mary Beard, professor of classics at Cambridge University, said she is very doubtful that the site will contain the tomb of Cleopatra.
"I would have thought it very unlikely that Marc Antony was buried with her. Of course, if the title 'Tomb of Cleopatra' was pinned on [this site], it would be a huge tourist attraction," she said.
"I am not, needless to say, impugning the archaeological credentials of Mr. Hawass, but it's hard not to think that such factors play some part in the enthusiasm surrounding this discovery."
Hawass has been digging at Taposiris Magna for the past two years and has explored about 95 percent of the site.
Excavations are now on hold and will resume in November, when the team plans to use radar to further map buried features.
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