The Exmoor adventurer, who lives near Exford, expects to reach the 29,000 feet summit at 03.30 BST on Saturday.
Sixty-four-year-old Sir Ranulph and his team set off at dawn for the Khumbu Icefall, one of the most dangerous parts of the route.
The route will take them across Western Cwm, a glacial valley, where they will stay overnight before tackling the six-hour, 650-yard climb to Camp Four.
Then, it will be a case of waiting for the right weather before completing the last part of the climb in around 12 hours, aiming to reach the summit on Saturday.
As the team heads closer to the mountain’s ‘death zone’, the air becomes thinner and the temperature plummets.
Sir Ranulph admits his main concern is exhaustion due to the altitude.
He said: “On past expeditions, particularly long polar treks pulling very heavy weights, the exhaustion factor has come in - but not nearly as bad as here because this is altitude exhaustion.
“So I need a mental defence against the wimpish voice in my head.
“At times like this one has an inner voice saying ‘stop, we have got to stop, it is not sensible to carry on’.
“That is when you need a mental defence. Mine has always been the memory of my grandfather and my father.
“Their spirits are around and watching and I do not want to do anything that will shame them, such as giving up unnecessarily early.”
Sir Ranulph holds several endurance records, among them the successful completion of seven marathons in seven days on seven continents.
Three years ago he was forced to abandon his first attempt on Everest after suffering a heart attack.
Sir Ranulph is raising funds for the Marie Curie ‘Delivering Choice Programme’, which was launched in 2004 with the aim of doubling the number of people who can die at home.
The charity wants to develop and help provide the best possible services for terminally ill patients, allowing them to be cared for in the place of their choice.
- Our photograph shows Sir Ranulph on his earlier Everest attempt. Photo submitted.