"The decision making phase has reached a critical point," confirmed team boss Christian Horner in Montreal.
"The data we gather this weekend is key. We want to make a decision by Austria."
Renault-powered Red Bull is able to closely compare the two manufacturers' data intricately, as junior team Toro Rosso already uses Honda power.
"We want the engine that gives us the best chances," Horner added.
In the wake of the McLaren-Honda fiasco, Renault might seem like the obvious choice for Red Bull.
But Toro Rosso's Pierre Gasly said: "Honda is not too inferior to Renault. But I hope this weekend that we close the gap even more to them.
"I am impressed by Honda's determination. They really want to prove that they have everything they need to produce the best engines in formula one. When they want something, they do everything to achieve their goal.
"I already saw from Super Formula that these are the most dedicated people I've ever worked with," he added.
Whatever decision Red Bull takes, it is rumoured the team is looking for a two-year contract in order to be free to welcome Porsche to F1 in 2021.