The Woking-based constructor, which is set to run Honda engines from 2015, have yet to announce their driver lineup for next season, with the 2009 world champion's place widely thought to be in jeopardy.
However, his manager Richard Goddard has claimed that the 34-year-old could join forces with Mark Webber to try to win the coveted Le Mans 24 Hours race and compete in the World Endurance Championship.
He told the Daily Mail: "Jenson is an incredibly competitive racing driver who wants to race. He's too good to sit at the back of the F1 grid, so he either gets a competitive car in F1 or he goes to get one elsewhere.
"The World Endurance Championship is a formidable series that is gaining strength, and Mark going there has added a lot."
British driver Button has claimed 15 Grands Prix victories since his debut in 2000.