But Boullier went into the Montreal weekend offering high praise for 34-year-old Button, the most experienced driver on the F1 grid whose contract runs out at the end of the season.
When asked on Thursday if that praise indicates a new contract is on the table, Button answered: "Er, no.
"No more progress at all. We both want to work together in the future but it's just not time yet."
On Saturday, Boullier agreed with Button that the time for contract talks is yet to arrive, but he also insisted McLaren wants to keep the Briton on board.
"I would love, when it is time, to sit down with him, to carry on with him, clearly, and as long as we can," the Frenchman told the British broadcaster Sky.
"With Kevin (Magnussen) as well. But I more and more appreciate working with Jenson, it's true," Boullier added.