We will not sell Toro Rosso during the 2008 season but it will be before 2010.
Renault's Robert Kubica and Toro Rosso driver Jaime Alguersuari were handed reprimands for two separate incidents.
Bourdais's move comes after he impressed Toro Rosso in a series of tests this summer.
Toro Rosso's Sebastien Buemi claimed sixth ahead of Williams' Nico Rosberg, with BMW Sauber's Robert Kubica eighth.
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Toro Rosso's Sebastian Vettel took the final points place, holding off Heikki Kovalainen's McLaren in the closing laps.
Toro Rosso said on Tuesday that Vettel would replace Speed, who was axed after the European Grand Prix.
Romain Grosjean claimed seventh, finishing ahead of Ferrari's Felipe Massa, Toro Rosso's Daniel Ricciardo and Red Bull's Mark Webber.
Toro Rosso tested Buemi, Bourdais and former F1 racer Takuma Sato last week.
Brawn's Ruben's Barrichello was seventh while Toro Rosso's Formula 1 debutant Jaime Alguersuari avoided any major incidents in 20th.
Toro Rosso are hoping the STR3 will make its full debut at next month's Turkish Grand Prix in Istanbul.
Toro Rosso have yet to confirm their 2009 drivers but a spokesperson said there was no deadline for a decision.
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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Toro Rosso's Sebastien Buemi, Vitaly Petrov of Renault and the Force India of Adrian Sutil completed the leading 10 cars.
It was a happier qualifying session for Webber's compatriot, Daniel Ricciardo who steered his Toro Rosso to a highly creditable seventh.
Toyota driver Timo Glock was fourth with Toro Rosso's Sebastian Vettel following up his win in Italy this month with fifth.
The issue was highlighted when strips of rubber started flying off Jean-Eric Vergne's Toro Rosso less than 40 laps into the race.
His new teammate Sergio Perez scored his first points for McLaren as he came home ninth ahead of Toro Rosso's Jean-Eric Vergne.
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For the second day running, Sebastien Buemi was fastest in Toro Rosso's 2008 car with a best lap of 1:17.591 at Jerez.
Behind Sebastien Bourdais in his Toro Rosso, Kovalainen will start 18th, his lowest grid slot since joining McLaren prior to last season.
"It is not a big secret that we have put Toro Rosso on the market, " he told the Swiss publication Motorsport Aktuell's website.
Force India's Paul di Resta qualified 10th ahead of Toro Rosso duo Daniel Ricciardo and Jean-Eric Vergne, while his teammate Adrian Sutil was 13th.
German Sebastian Vettel has been promoted to the senior Red Bull team, while his 2008 Toro Rosso team-mate Sebastien Bourdais may not be retained.
Buemi, Red Bull Racing's reserve driver, has been strongly linked with a seat at Toro Rosso, who are now 100% owned by Red Bull.
Mateschitz said the Toro Rosso line-up would be confirmed "before the last test in December", which is at Jerez in southern Spain from 15-17 December.
Toro Rosso will use the same car as Red Bull, but fitted with a Ferrari engine rather than the Renault used by their parent team.
He also tested for Toro Rosso at Jerez in September and will return to the circuit as the teams undertake the penultimate test of the year.
Button was one of those linked to Toro Rosso and their decision means the Englishman's hopes rest with a rescue package for the collapsed Honda team.
Mosley upped the ante when he began legal proceedings against Ferrari, McLaren, Renault, BMW Sauber, Toyota, Brawn GP, Red Bull Racing and Toro Rosso on Friday.
Nick Heidfeld was seventh for a resurgent BMW Sauber, with Ferrari's Kimi Raikkonen eighth, followed by the Williams of Kazuki Nakajima and Toro Rosso's Sebastien Buemi.
Vettel took the first victory for a Red Bull-designed car last year when he won the Italian Grand Prix while driving for junior team Toro Rosso.
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