Sargeant's future at Williams has been in doubt in the wake of a run of accidents since the summer break.
He crashed heavily in qualifying and the race at the Dutch Grand Prix, hit the barriers at the Singapore GP, and then went off in a big accident during Q1 for the Japanese GP last weekend.
Those run of incidents come at a time when Williams wants to see the American show steady improvement over the remainder of the campaign to show that he can step it up alongside Alex Albon next season.
While Sargeant's latest crash prompted early speculation that Felipe Drugovich, Liam Lawson or Mick Schumacher could be in the frame to replace Sargeant, Vowles has poured cold water on any talk that he is definitely looking elsewhere for his team's second seat.
Instead, speaking on his post-race 'Vowles Verdict' video on the Williams website, he declared that the team wanted Sargeant to succeed – and that it had to work with him to make it happen.
"Logan has very clear targets that he has to hit before the end of the season and we're working with him continuously," said Vowles.
"That's the important point: we're working with him. We want him to succeed, and we want him in the car next year. This is very much on us as well.
"We have taken someone straight from Formula 2 without any significant testing, put a day and a half in Bahrain in this car, and then wished them well on a season that has been awfully challenging for rookie drivers, full stop."
Source: Autosport