The 69-year-old has been at the helm of the company since 1980, but a recent failed takeover attempt has seen fellow investors looking to oust the former Cooper and Brabham mechanic.
Britain's Daily Mail claims that Dennis will be told later today (Tuesday) that he must accept a lesser role or be axed altogether.
When asked to comment, team boss Eric Boullier stood by his boss, insisting: "Ron is chairman and group CEO of McLaren today."
But F1 supremo Bernie Ecclestone appeared to confirm Dennis' impending exit.
"It's a shame because Ron is part of Formula One. I hate to see him go," he told Spanish broadcaster Movistar.
"Maybe the board will change its mind and Ron will stay," he added.
Bahrain International Circuit - Winter testing