Much of the movement in the F1 driver market looks set to hinge on whether or not Ferrari retain Kimi Raikkonen for the 2016 season. If the Italian outfit decide to part ways with the Finn, it would trigger a number of moves in the rest of the grid.
Williams' Bottas is the man widely tipped to replace Raikkonen, with reports suggesting that Ferrari and Williams have discussed the possibility of Bottas joining Sebastian Vettel at Scuderia, but that no deal has been reached.
It is believed that Williams intend to retain Felipe Massa, and so will only have an empty seat if Bottas moves on to greener pastures. Should he do so, Button has been linked as a possible replacement.
The Briton started out in F1 with the Grove-based squad before moving on to first Benetton/Renault and then BAR (which would later be known as Honda and then Brawn) before joining McLaren.
However, the 35-year-old insists that he has not given any thought to where he will end up next season.
"I've had a lot of questions thrown at me about what I am doing next year but I have not thought about anything, seriously," he said.
"I just have to get my head down and concentrate on improving the car and then in a couple of months we will sit down and talk about next year."
It is not yet certain that McLaren will offer Button a drive for the 2016 campaign, with some reports suggesting that the 2009 World Champion could be replaced by reserve driver Kevin Magnussen, who raced for McLaren in 2014, or Stoffel Vandoorne, who is currently leading the GP2 championship and whom big things are expected of.