Absolutely none. There were some surviving mammoths in historical times, but they were a small population of dwarf mamoths on Wrangel Island, one of the most isolated places on earth. The evidence points to their extinction around 1600 BC, just as humans first settled in their habitat. It's possible that humans hunted them to extinction, but more likely the same climate changes that made it possible for humans to arrive hurt the mammoths' ability to survive.

In either case, humans and the Wrangel Island mammoths only interacted briefly; it's virtually impossible that any mammoths were brought to Egypt, let alone a breeding population. It also does not make sense to use Arctic animals as pack animals when the Egyptians had plentiful human labor and their own domesticated animals.

There is no evidence for mammoths at all in Africa or Middle East during the Old Kingdom; the last ones appeared millenia before, though they could be found much farther north until the 15th century BC.