Button emerged as a surprise player in this year's 'silly season' over the Belgian GP weekend when it was disclosed that McLaren are yet to exercise their option on the Englishman for the 2014 season.
However, according to The Times, 'The team mark 50 years in Formula One next week and an announcement that Button's £12 million-a-year contract has been renewed could coincide with the celebrations. The deal is likely to be for three years, taking Button to his 36th birthday.'
Button joined McLaren in 2009, just weeks after winning the World Championship with the Brawn outfit which has since morphed in to Mercedes.
Having previously driven for Williams and Renault, the Englishman is currently the most experienced driver on the grid.
"It's obviously not going our way at the moment, but it will, and I'm very happy here, I feel good here, and I still feel we can achieve so much together," Button told The Daily Mail.
"I'll be here for my future in Formula One."
Of the frontrunners, only McLaren and Mercedes are expected to retain their current driver line-ups for next season, with changes predicted at both Ferrari and Lotus while Red Bull are certain to make one alteration following Mark Webber's announcement he will retire from F1 at the end of the season.