Ilmor and Advanced Engine Research (AER) have thrown their names into the hat to supply F1 with budget engines while Cosworth have said no.
The FIA recently began the process of searching for a supplier for cheaper customer engines for Formula 1.
At present the 1.6-litre turbocharged V6 engines cost around £15-20million per season which is more than double of the previous V8s.
Motorsport's governing body wants to bring those costs down with a budget engine, signing an "exclusive alternative engine manufacturer which will be solely entitled to supply this alternative engine" from 2017 to 2019.
Ilmor and AER have both put their names forward.
Ilmor design guru Mario Illien, who is reportedly set to help Red Bull with their engine plans in 2016, told German publication Auto Motor und Sport: "Ilmor has applied for it."
Meanwhile Britain's AER said they are also keen.
"AER are very interested in the proposal from the FIA," founder Mike Lancaster told Motorsport.com. "We're putting in a submission for it.
"The request seems to fit nicely with our latest V6 GDI engine. They're looking for something which produces a lot of power, and we have an engine that can do that.
"The WEC engine is the P60, the engine we're proposing is called the P66, which is a higher revving version of that. It will be ideal for the job, we believe."
Cosworth, however, have said no.
With the engine contract running for three years, 2017 to 2019, Cosworth co-owner Kevin Kalkhoven feels it is not economically viable for his company.
He told Motorsport.com: "We looked at the economics of developing an engine from scratch, which is what we would have to do.
"The economics of it just don't work out. It would cost roughly £20m to develop from scratch, with everything else that goes with it. You've also got to pay for the on-track support, as well.
"It's also too short a time to produce an engine unless you've already got a design."