The VERY, VERY, very south of Egypt might, at one time, have bordered on the more northern African forests. They were all "rain forests" because that kind of forest could not have existed without almost daily heavy rainfall.
But that is a far cry from an Egyptian "rainforest."
Egypt might have extended its rule farther south than we know of as well. However, by the time there was the culture WE KNOW OF in Egypt, it was desert. We also know this information from the other ancient civilizations at the time...ones the Egyptians warred against.
It IS an interesting topic. Rain forests and whale bones, what could be more interesting for a Sunday night?
I don't know about rainforests in Egypt, but there is a theory that the Sphinx predated the ancient Egyptians by several thousand years when the climate was much wetter there than it is today. This theory was based on the fact that wind erosion is very different from water erosion and water erosion patterns can clearly be seen on the limestone of the Sphinx and in the Sphinx Enclosure, but not on other Egyptian works on the Giza plateau. The last time there was significant rainfall in Egypt was over 9,000 years ago - thousands of years before the Old Kingdom when the Sphinx was supposedly carved.