Button, 34, earlier reacted coolly to Dennis' claim he should "try harder", and in a subsequent interview he insisted he is "not thinking about" the future yet.
"Anyway, I can't talk about contracts," he is quoted by Speed Week. "No driver can."
As for the Spanish sports daily Marca's claim that Dennis has told Button he has no place for 2015, a McLaren spokesman dismissed it as "complete nonsense".
Ultimately, Button may be granted at least one more year in silver, with team boss Eric Boullier admitting McLaren may not be ready for a truly top driver like Fernando Alonso, Sebastian Vettel or Lewis Hamilton.
"Currently, we only want to find out what situation they (other drivers) are in," the Frenchman is quoted by Speed Week.
"Because it's about the total package. So it is not a question of having a world champion in the car at any cost.
"You don't want that if your car is two seconds slower than the best -- it would not only be expensive, but also difficult to handle.
"We will decide when everyone is ready," Boullier said.