The Japanese manufacturer has been plagued with unreliability since pre-season testing and has been working on revising its engine as it still has a power deficit to rival manufacturers Mercedes, Ferrari and Renault.

It had hoped to introduce its first major performance upgrade in Montreal but is running out of time to complete testing and prove durability.

"I don't give up and we are trying very hard [to be ready] but until Thursday [before the race], I can't decide," said Honda chief Hasegawa.

"Already, we have had some performance [from the update], but if it is very small, it's not worth changing engine for the next one.

"We haven't started working on the settings. If we are not confident enough to set up that specification, it will cause some driveability issues, so the settings are also important.

"We have some other elements in development, we can introduce it if we can set up and if we can check the reliability. Everything is not ready. But we have some factors (that are).

"Maybe we stick with the next step of the engine, even if the next step up is very small, or can we try another step up in performance? It's very tight to introduce a big update for Canada."

Hasegawa says the update is focused on the internal combustion engine (ICE) with tweaks also planned for the turbine.

"The ICE is the biggest area we need to improve," he added.

So far this season, Honda has only changed engine maps, made reliability tweaks and introduced revisions to its induction and fuel system.

McLaren is the only team that has yet to score points this season, with team boss Eric Boullier saying a boost in performance from Honda is key to the alliance making progress.

"If there was a level playing field between engine performance we would be comfortable now to be high end," he said.

"We need that step from our partner for the second half of the season to deliver strong performance and score points."