What is the greatest recorded distance that a person has driven in one day?

Here are the fastest cars in the world.
http://www.thesupercars.org/fastest-cars/fastest-cars-in-the-world-top-10-list/

If you drove one of these flat out for 24 hours, you could travel between 6200 and 6400 miles. So that sets your upper limit. My guess is that is probably closer to 2000.

Le Mans annual 24-hour race. Over the 24-hour period modern competitors will complete race distances well over 5,000 km (3,110 mi). The present record is 5,410 km (3,360 mi), recorded in the 2010 race.[4] It is a distance over six times longer than the Indianapolis 500, or approximately 18 times longer than a Formula One Grand Prix.
https://en.wikipedia.org/wiki/24_Hours_of_Le_Mans
Of course this is for a single car, not driver, but if there were two drivers one might have done more than the 1700m reported in the previous answer.

3,438 km in 23 hrs 15 min (2,136 miles)

At the 1950 Le Mans 24 hour race, Louis Rosuier drove the car for 23 hrs 15 min (254 of 256 laps). His son Jean-Louis Rosier drove the other two laps. The car travelled 3,465.12 km during the 24 hours .. deduct 2 x 13.492km track length = 3,438.13km travelled in 23 hrs 15 min by one driver (2,136.4 miles).

http://www.experiencelemans.com/contents/en-us/d183_1950_Le_Mans_24_Hours_Competitors_and_Results.html
https://en.wikipedia.org/wiki/List_of_24_Hours_of_Le_Mans_winners