Peraud made a strong move on stage 17 as the Ag2r-La Mondiale rider finished fourth to move to within 42 seconds of Movistar's Valverde, who sits second in the general classification.
Valverde lost 49 seconds to Peraud on the 124.5-kilometre ride from Saint-Gaudens to Saint-Lary Pla d'Adet as the Spaniard crossed the line in 10th on Wednesday.
It is another French rider, FDJ.fr's Thibaut Pinot, who occupies third spot, but Valverde is most concerned by Peraud.
The 37-year-old has been French time-trial champion in the past and the penultimate stage of this year's race is where Valverde expects him to launch his challenge for the podium, rather than on stage 18 to Hautacam.
"It's true that I have close rivals in Pinot and Peraud," said Valverde. "But Peraud is the one I fear the most because he's very good in time trials.
"I know Hautacam well. It's going to be a very hard day, especially after the two days we just had.
"We're going to try and recuperate because tomorrow is another important day."