An International Automobile Federation (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 their preparations to join them 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 who joined in 2010, only Marussia remain despite missing the last three races of 2014 due to financial problems and then coming out of administration by the skin of their 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 $5,000 (£3,206). Full applications were due to be submitted by Sept 1 with a total fee set at $130,000.
(Editing by Tony Jimenez)
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