An FIA spokesman said on Monday that neither of the two applicants who had responded to an FIA tender had satisfied the criteria and the process was closed.
No details were given on the identity of the latest applicants.
Formula One currently has 10 teams with Haas already advanced in its preparations to join the fold in 2016 with Ferrari power units.
The FIA had launched a tender in May to try and attract more teams from the start of 2016 or 2017 at a time when some of the current entrants are facing an uncertain future.
The sport has not had 12 teams, and 24 cars, since the end of 2012.
Of the three teams that joined in 2010, only Marussia remains despite missing the last three races of 2014 due to financial problems and then coming out of administration by the skin of its teeth.
Spanish-owned HRT went out of business in 2012 and Caterham, set up by Malaysian aviation entrepreneur Tony Fernandes, folded after going into administration last season.
The FIA had hoped to identify a new “candidate team to participate at a competitive level” in a bid to boost the number of cars on the starting grid without resorting to other measures.
Expressions of interest had to be registered by June 30, the deadline later extended to the end of July, with an initial non-refundable fee of $5000 (R64 500). Full applications were due to be submitted by September 1 with a total fee set at $130 000 (R1.68m).
Original source: Formula One's new team hunt fails