In a bid to hand the Russian valuable mileage ahead of his F1 debut with the team, Toro Rosso wants to get him in action at the final two races of this campaign.
It is planning to get him to run in first free practice at both Austin and Interlagos - providing he can get a mandatory superlicence in time.
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To do that, Toro Rosso will test him in a two-year-old car over the next few weeks so he can complete the minimum 300km of running over two days that he needs to show the FIA he is worthy of a superlicence.
Kvyat completed half a day for Toro Rosso at the Silverstone young driver test earlier this year, and recently took part in a straightline test for Red Bull.