Jenson Button could be a Williams driver in 2017, with deputy team principal Claire Williams stating the Briton is an "attractive option".
Button's contract with McLaren finishes up at the end of the current Formula One season, with uncertainty surrounding his F1 future.
The 36-year-old was expected to retire at the end of the 2015 season, but decided to extend his stay at McLaren for one more year.
However, Button may make the switch to Williams next year, the team for which he made his F1 debut as a 20-year-old in 2000.
"It would be lovely [to have Button back at Williams]," Williams told Autosport. "The story is great.
"There are some great talents out there and Jenson is very attractive commercially as well.
"He is also an extremely intelligent driver from a variety of different angles so of course he is going to be up there for consideration.
"When I went to Silverstone and I was on the big stage, Tony Jardine who was the MC said to the crowd: 'Tell Claire how much you'd like to see Jenson back in a Williams'.
"The whole place erupted. It was extraordinary.
"We are still evaluating our options. You want to make sure you evaluate every area that you put weight on when you are choosing a driver, not just what they do on a Sunday afternoon but it's everything they bring to a team."
With Felipe Massa and Valtteti Bottas' deals expiring at the end of the season, Williams have whittled their options down to several drivers.
"You start off with a long list and you work down to a shortlist," Williams said. "We're on the shortlist at the moment and now it's just a case of choosing the two drivers.
"We wouldn't want to leave it any longer [than a couple of months to make a decision]. From a stability perspective, we want to know where we are all at.
"It's not a decision of a moment choosing who you are going to put in your cars as they are a big part of what we do.
"The top teams have made their selections so we now are the team everyone is looking at if you are drivers that haven't got a contract next year.
"We have options available to us and that's great, it's a wonderful position to be in and because we have those options, we need to make sure we make the right decisions."