Baku, June 4, AZERTAC
Button, who began his Formula One career at Williams in 2000, is out of contract with McLaren at the end of the year, according to Daily Express.
And with Stoffel Vandoorne, the highly-rated McLaren reserve driver who deputised for Fernando Alonso in Bahrain earlier this year waiting in the wings, Button may be without a seat for 2017.
Button began his career with Williams as a 20-year-old, and a move back to the Grove-based team for one final hurrah could be seen as the perfect bookend to his world championship-winning career.
But asked if speculation linking Button to Williams was unsettling, Massa said: "For sure not. We all know about rumours in Formula One, and I am zero scared and worried about anything.
"I am really happy working for Williams. This is a team which gives me a lot of pleasure to work for, and I see the same with them working for me.
"It would be nice to stay, but it would be nice to stay in a team where you really see that you can do a good job and have a good future. I am ready for everything."
Massa, the only driver to finish in the top 10 at every race this season, joined Williams in 2014 after a long association with Ferrari which saw him miss out on the title to Lewis Hamilton by just one point in 2008.