Williams are keen to pursue a romantic move for Button, which would see the 2009 world champion return to the team with whom he started his grand prix career.
Button, 36, is out of contract with McLaren at the end of the season, but the British team have already announced they will not make a decision on their driver pairing for 2017 until September at the earliest.
Fernando Alonso has one year to run on his deal, while reserve driver Stoffel Vandoorne is waiting in the wings should McLaren terminate their seven-season relationship with Button.
In such a scenario, it is understood Williams would be prepared to prolong Button’s career into an 18th successive campaign.
However, as Formula One heads for its summer shutdown, deputy team principal Claire Williams said: “I am not sat here waiting for [McLaren chairman] Ron Dennis to make his decision or for Jenson to make his decision.
“It it is not about what other people are doing.
“I am not going to be waiting around, because that is just not the right mentality for a team like ours to have.
“It would be a great story, but he has to make the right choice for him, and we have to make the right choice for the team.”
Doubts remain as to the Grove-based constructor’s ability to afford Button, who currently earns around £12m a year.
Button’s commercial appeal, though, is a huge attraction to Williams as they pursue sponsorship for 2017.