Alonso drove for Minardi last year and has secured a seat at Renault next season.
"He didn't have the necessary mileage in championships that the FIA recognises, " said a Minardi spokesman.
"It's theater, " says Christina Minardi, a Whole Foods regional vice president who oversees the New York stores.
Midland have signed Dutch driver Christijan Albers from Minardi and are expected to continue with Portugal's Tiago Monteiro.
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Wada wants the FIA to impose stricter limits on Minardi, now known as Scuderia Toro Rosso following Red Bull's buy-out.
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Paul Stoddart, the former boss of F1 team Minardi, said the sport was left "without credibility" while Max Mosley remained in charge.
Minardi were not given the chance to put their spare car into action as test driver Bas Leinders was not given permission to compete.
Mateschitz bought the team, then known as Minardi, in 2005 from Paul Stoddart before selling a 50 percent stake to the former grand prix winner Gerhard Berger.
Alonso made his F1 debut for Minardi in 2001, moved to Renault as their test driver in 2002 and was promoted to their race team in 2003.
When the new rules were introduced, world governing body the FIA gave Minardi permission to use old V10 engines, subject to rev limits, due to their financial problems.
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However, there has been speculation that Herta might race for Minardi at the US Grand Prix in September, as well as in other races towards the end of the season.
Justin Wilson was 19th for Minardi, saved from starting last by Sauber's Nick Heidfeld who hit technical problems at the first corner and stalled in front of thousands of his countrymen.
Only Jaguar, Arrows and Minardi have vacancies - and Jaguar are considered certain to sign Mark Webber in place of Eddie Irvine alongside Pedro de la Rosa, as exclusively revealed by the BBC.
But in 2005, controversy blighted the race as a result of the Michelin tyre safety row which meant that only six cars were on the starting grid - those of Ferrari, Jordan and Minardi.
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Minardi boss Paul Stodddart - who has seen Renault's Fernando Alonso, Webber and now Wilson move on to bigger things - is to replace Wilson in Hockenheim with Dane Nicolas Kiesa, winner of the Formula 3000 race in Monaco this year.
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