With 2,591.1km of the race’s 3,414km distance covered, Swift’s Arkea-Samsic team have a realistic prospect of carrying one of the coveted leaders’ jerseys to the finish line on the Champs-Elysees, in Paris on Sunday.
That would be a significant prize for a squad reduced from eight to just three riders because of crashes and the punishing nature of this year’s event.
Having featured in two breakaways earlier in the race, Swift’s task over the next few days will be looking after team-mates Nairo Quintana and Elie Gesbert.
“In the days coming up I can’t really do a great deal, it is just bottle duties or helping out Nairo or Elie, who can climb a lot better than me,” said the 25-year-old, from Thorne.
“They can both definitely chase stage wins in the next few days and Nairo is also chasing King of the Mountains points.
“He is only 10 behind [leader] Wout Poels, so that is definitely within sight.
“If either of those two are in the bunch when I am there it’s just a case of helping move them up a bit or get them some bottles or food, or just placement at the beginning of the day before the breakaway goes.”
Swift is 77th in the general classification, two hours and 12 minutes behind yellow jersey wearer Tadej Pogacar.
If he can survive the Pyrenees, he will be confident of riding into the French capital this weekend.
Looking ahead, he said: “It is not far away now.
“I feel like the next six days will pass pretty fast. We’ve got three days left in the Pyrenees, a sprint stage, time trial and the last day.
“There’s only three major days left in the race, so with Paris just around the corner there is a bit of extra motivation there.”
But Swift, who made his Tour de France debut last year, admitted: “I am pretty tired.
“I was speaking to [four-time winner] Chris Froome two days ago and he was saying it’s the hardest Tour de France he has been in.
“It has been a crazy race, but it has been that way all season; all the races are full gas; because of the pressure from Covid, with races being cancelled last year and with sponsors being quite limited, everyone just wants to perform.
“It makes the level just that bit harder and there are no easy days, so I was thankful of the rest day.”
Once the mountains are completed, attention will turn to whether British rider Mark Cavendish can surpass Eddy Merckx’s career record of 34 Tour de France stage wins, having equalled it with his fourth victory of the current edition last week. Swift predicted: “He has matched it and there’s two sprints left so I can see him breaking it, for sure.”