Evenepoel capitalised on Jonas Vingegaard's withdrawal from the race on Sunday, after the Dane broke his collarbone in a crash, and eventually claimed a stage win at the Plateau de Solaison to move up to second in the general classification.
While the Belgian is trailing yellow jersey holder Pogacar by five minutes, he has a 58-second lead over Mexico's Isaac del Toro, racing for UAE Team Emirates-XRG, who sits in third.
With his reputation as the world's best time-trialist, the Red Bull-Bora-Hansgrohe rider is expected to extend his advantage over the other podium contenders in the 26.1-km stage from Evian-les-Bains to Thonon-les-Bains.
"I will try to go again for a stage," the 26-year-old rider, who has won an ITT stage in each of the two previous editions of the Tour, told a press conference on Sunday.
Even Pogacar considers Evenepoel as the favourite for stage 16.
"He has his day on the time trial. I think he is a big contender," the four-time Tour winner told a press conference on Sunday.
The ITT route features a 9.7-km climb at an average gradient of 4.3%.
"There are nine kilometres of climbing, eight kilometres of descent and nine kilometres of flat terrain so it’s quite a comprehensive time trial," the race organiser's sports director Yannick Talabardon said, adding that "there's no point in changing bikes" for the climb.
"The final section consists of long straight lines in Thonon-les-Bains," he noted.
As the Tour enters its last week, which features three gruelling mountain stages in the final four days, Tuesday's time trial will be critical for riders aiming to secure podium positions.
Evenepoel, who has already showcased his climbing strength and ITT dominance, is well-positioned to make further gains.
With Pogacar holding a commanding lead, the main battle may now centre on the fight for second place, where Evenepoel's time-trial expertise could prove decisive.