Sargeant is the favourite to secure the final spot on the 2024 F1 grid with Williams despite a mixed rookie campaign.
While he showed signs of improving form throughout the year and scored a point at the United States GP, there were also some notable errors that resulted in big crashes.
But Williams has been consistent in feeling that Sargeant needed time to prove himself, so would be given until the end of the season to show what he could do.
And with him securing a season-best seventh on the grid for the Las Vegas Grand Prix, Sargeant appears to have done enough to convince Williams he is worth sticking with.
However, Vowles wants to have one final dig into the analysis of the season to get a comprehensive picture of Sargeant's form before he commits to a fresh deal.
Asked when a decision would be made, Vowles said: "Shortly. Within weeks of where we are now. Fundamentally, I wanted to make sure I saw the end of the season and assess all the options.
"I'm someone that was very clear from the beginning. I want to assess this across the season, not across one race, to make sure we make the right decision for this team and for the future of Logan as well."
Vowles said that while Williams did have other options available, there were "not many" candidates, as the emphasis was clearly on just double-checking where things were at with Sargeant.
"I just want to check through a full season of data one more time and look at the progress, look at mistakes, look the outliers, look for growth and just make sure we're on the right track," added Vowles.
Speaking at last weekend's Abu Dhabi Grand Prix, Sargeant said that he had not been spending time worrying about the contract situation for next year.
With Vowles having been clear that he would wait until after the end of the season to make a call, Sargeant said that he felt things had been going in the right direction.
"I feel like from a driving point of view, everything's been getting much better in the past for however many rounds," he said.
"And yeah, I'm just trying to do my job the best I can. I think with how it's been going recently, I don't see any issues."
