Sainz has been in talks with a number of teams, including Red Bull, but they opted to re-sign Sergio Perez on a fresh two-year deal.
The Australian Grand Prix winner is looking increasingly likely to have to find a drive at the lower end of the grid, with Mercedes said to be prepared to back young F2 driver Kimi Antonelli to replace Hamilton.
Why would Sainz join Williams?
Williams are at the bottom end of the constructors' championship, and only picked up their first points of the season at the Monaco Grand Prix.
However, they do appear to be making progress, with Vowles' impact since his move from Mercedes credited to some of this.
Explaining why Sainz might opt for Williams, Vowles told Sky Sports: "There’s a reason why I’m here. Williams isn’t the same Williams it was three years ago and by the definition of the fact that we’ve been talking to Carlos shows you that we’ve changed our approach.
“We want two world class drivers to be a part of our staple going forward. We want the world to realise that we are here and we’re serious. We’re investing what it takes to be back at the front.
Two years from now, F1 will be in its first season of a new era, as fresh regulations targeting sustainability, new engines, and better racing come into play.
“In 2026, we have one of the best power units, if not the best power unit coming to our car. We’ll announce, shortly I hope, there’s around about 30 incredible people from other teams joining our organisation that we’ve been gathering across the last 12 months.
“The world is changing and someone like Carlos would feature very highly in that regard in terms of the ground picture of where we are. Of course, the difference is he has the choice of whether he wants to come here or not and that’s his to make.”
But is that pitch good enough to convince three-time race winner Sainz?
“It’s hard to tell," Vowles admitted. "I think he can see all the strengths. I think it’s easy for me to say because I’m Williams and I wear the shirt. I think it’s an easy decision to come here, but it has to be his to make.”