Specifically, the rumour in Singapore is that Toro Rosso owner Red Bull will assess Honda's performance at the junior team next year and potentially decide to switch to Japanese power for 2019.
The speculation also comes amid rumours that Renault has already told Red Bull that it is not willing to supply them with French-made engines beyond next year.
"Obviously that is speculation at this point in time," Renault boss Cyril Abiteboul said.
However, the Frenchman also did not deny that the story had truth in it.
Red Bull team boss Christian Horner, on the other hand, tried to divert the speculation in Singapore by hinting on British TV that the team might actually be powered by Aston Martin in 2019.
"No," said the Briton. "I was asked a question about Porsche coming into Formula 1 and I answered that very clearly we have an existing relationship with an OEM that don't make F1 engines, and obviously that will continue."
Yet he did admit that Red Bull will watch the progress of Honda-powered Toro Rosso very closely next year.
"At Toro Rosso, the pressure will be lower for Honda than it was at McLaren, so they'll be able to work on their problems in peace," said Horner.
Asked specifically if Honda is targeting a Red Bull tie-up for 2019, senior Honda representative Masashi Yamamoto said in Singapore: "If there is a chance in the future to supply engines, why not?"
However, he did deny rumours that Honda is buying Toro Rosso from Dietrich Mateschitz.