The restored Douglas C-47 transport plane, known as Whiskey 7, is displayed in the US National Warplane Museum in New York and has been invited to Europe to mark the anniversary in June.
The plane will make the journey over a series of shorter flights landing in Newfoundland, Greenland, Iceland, Scotland and Germany before flying over Sainte-Mere-Eglise near Normandy.
Museum officials believe the plane is the only C-47 still flying and compared the journey to France to trying to drive a 70-year-old car thousands of miles without a breakdown.
Erin Vitale, chairwoman of the Return to Normandy Project, said: "It's going to be a huge challenge.
"There are very few of these planes still flying, and this plane was very significant on D-Day. It dropped people that were some of the first into Sainte-Mere-Eglise and liberated that town."
Once in France, the crew will meet up with 89-year-old Leslie Palmer Cruise, one of the original paratroopers to be dropped from the aircraft.
The National Warplane Museum president Austin Wadsworth said a further 70,000 dollars (£42,400) needs to be raised to reach the 250,000 dollars (£151,600) needed to fund the restoration and journey to Normandy.
Most of the money has been spent on rebuilding two engines with a modern GPS systems also installed.
Mr Wadsworth said: "The avionics in the airplane are modern. We're not going to go with what they had in 1943. They would have had probably a radio beacon receiver and a lot of dead reckoning."
There is still no autopilot on the aircraft with five pilots set to share duties on the journey to Europe.