The Azkoitia-based team are one of three major contenders looking to enter F1 as the 13th team next season along with the Jacques Villeneuve/Durango bid, and Serbian-based outfit Stefan GP.
And with development of their chassis already going through the wind tunnel, they would appear to be the most advanced of the three bids.
The FIA has already rejected a number of bids to join motorsportÃ¢â‚¬â„¢s elite, but the remaining contenders have been invited to Paris for a meeting on 13 August.
Epsilon is headed by Joan Villadelprat, with former Williams and Sauber engineer Sergio Rinland on board as chief engineer.
Speaking about their recent developments, Rinland said: Ã¢â‚¬Å“We have tested our model for the first time in the wind tunnel last week.
Ã¢â‚¬Å“Everything looked fine and we are already well underway with our design now.Ã¢â‚¬Â
The Villeneuve/Durango and Stefan GP bids have yet to reveal much in the way of technical detail, with the former Toyota TF110 chassis, gearbox, engines and technical support all up for grabs from the former F1 team.
Current backmarkers Hispania have been linked with the Toyota designs, but their funding issues have ruled them out of a realistic sale.
Villeneuve/Durango are rumoured to be well-financed, with Libyan oil company Tamoil just one large firm believed to be supporting the bid.
The Villeneuve/Durango bid was the last of the three contenders to be announced, but any team bidding to join the sport will be extremely limited in time to develop a car.
The FIA is set to announce which bid has been successful following the meeting in Paris later this month.
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BIOGRAPHY: Mohamed Salah