Dr Helmut Marko says he is "confident" Red Bull's engine supply crisis will finally end this weekend in Austin.
If it is not solved, team owner Dietrich Mateschitz's end-of-October deadline will arrive and the Austrian billionaire could pull the plug on the sport.
"It would suck," Daniel Ricciardo, the lead driver of the senior team Red Bull Racing, told the Guardian newspaper.
On the face of it, Red Bull is out of options. Mercedes and Ferrari have said no and the relationship with Renault is poisonous.
F1's only other engine supplier, Honda, has also ruled out adding a customer team for 2016, but Autosprint correspondent Alberto Sabbatini says there is a faint hope of a deal with the Japanese manufacturer.
He explained that Red Bull got itself into the situation because it intended to hook up with Audi from 2018, but Mercedes and then Ferrari got wind of the project and baulked at being a mere stop-gap solution.
Then, VW's diesel-gate scandal struck and Red Bull was left with nothing.
Autosprint reports that Honda could be a lifeline for Red Bull, as the energy drink marque could help Honda develop its struggling hybrid technology, even though works partner McLaren "is strongly opposed".
In truth, the more realistic solution for Red Bull is simply to somehow patch up its almost terminal relationship with Renault.
"There will be a meeting in Austin," Marko, Red Bull's closest F1 official to Mateschitz, told Osterreich newspaper. "I am confident that we will find a solution."
The report cited insiders who believe the most likely outcome is that Red Bull will stay with Renault while Toro Rosso switches to 2015-spec Ferrari power.
When asked what he thinks will happen, Mercedes' Toto Wolff answered: "I don't know.
"I am not part of the management of Red Bull," he told the Spanish sports daily Marca.
"In the last two months we have heard of various ideas but I cannot judge. It seems that they are talking with Renault, and for F1 it would be good if they continue."
Bahrain International Circuit - Winter testing