Contador, the 2007 and 2009 champion, heads into Saturday's 52-km course between Bordeaux and Pauillac with an eight-second advantage over Luxembourg's Schleck.
"Tomorrow will be the most important day of my career, I have nothing to lose," Schleck told reporters after Friday's 18th stage.
"I still believe I can do it. It will be decided more in the head than in the legs."
Eight seconds may look like a slim margin, but Contador's superiority in the time trial over the Saxo Bank rider is overwhelming, although the Spaniard is taking nothing for granted.
"It will be an incredibly hard day, it's not a time trial like the others, it comes after three weeks of racing," the 27-year-old said.
"It will be more a matter of the strength you have left and Andy is strong."
Swiss Fabian Cancellara, the time trial world and Olympic champion, is the favourite for Saturday's 19th stage and other contenders include Briton Bradley Wiggins, who has been struggling throughout the race.
"I will be putting everything into that last time-trial and salvaging a stage win which would transform the whole perception of the race that I have had," said Wiggins, who hopes to hand Team Sky their first win on the Tour.
Saturday's time trial will also be Lance Armstrong's last in the Tour, a race he won a record seven times.
"We're close now. I'll do a hard TT tomorrow, then team diner on Sunday and Monday... Onward," said 38-year-old Armstrong, who lies 23rd overall, 37:58 off the pace.
(Editing by Justin Palmer; To query or comment on this story email email@example.com)