Paul di Resta and even Kamui Kobayashi have also been named as possible replacements.
Briton Paul Di Resta took the final point in 10th place in the second Force India.
Di Resta signed for Force India in January after winning the team's support last season as their reserve driver.
Nico Rosberg of Mercedes finished seventh with rookie Paul Di Resta in eighth in the second Force India car.
Force India's Paul di Resta finished qualifying in fourth but was penalized five grid places for changing his gearbox.
Force India's Paul di Resta secured an impressive fourth position ahead of Mercedes driver Nico Rosberg and Lotus's Kimi Raikkonen.
Scotsman Di Resta and German Adrian Sutil helped take the wraps off the new car at the team's Silverstone base.
Scot Paul di Resta chose not to set a time in final qualifying and will line up 10th for Force India.
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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.
Coulthard has witnessed Di Resta's potential at close quarters, and is eager to help his compatriot make the best possible start to his F1 career.
Di Resta took his first steps in F1 last season when he was signed as Force India's reserve driver, taking part in eight first practice sessions.
"We've got high aims of finishing in a good constructors' championship position and I know that I've got to play my part in this, " Di Resta said.
Toro Rosso driver Daniel Ricciardo put in a strong performance for a career-best seventh place, finishing ahead of Force India's Paul di Resta, Lotus' Romain Grosjean and Hulkenberg.
"In 16th- and 17th-century Flanders, it was all the rage to collect odd items from around the world and display them in ornate verzamel cabinets, " Van Steenbergen-di Resta said.
The only remaining vacancies, apart from the second Hispania seat, are now at Force India, who are expected to opt for Germany's Adrian Sutil and Briton Paul di Resta.
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Nico Rosberg qualified in seventh ahead of team-mate Michael Schumacher for Mercedes, while the two Force Indias of Adrian Sutil and Paul di Resta slotted in in ninth and 10th.
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The Force India duo of Paul Di Resta and Adrian Sutil will start fifth and sixth respectively, while Lotus' Kimi Raikkonen -- who was fastest in Friday's practice sessions -- will be eighth.
Di Resta, who has been promoted from his role as reserve driver, did not improve on that time, and ended the day 10th fastest out of 11 runners after a trip into the gravel at Turn Nine.
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Jenson Button's miserable weekend looked set to continue as he drifted from 14th to 17th, although he salvaged some pride with a credible eighth-place finish, holding off a late surge from teammate Sergio Perez to finish behind Paul di Resta.
Scot Paul di Resta had his first taste of the new Force India which he will drive in his debut season and when the team stopped for lunch, he had managed a best of 1:22.945, then the ninth fastest time, after what the team said on the social network site Twitter was due to work on brakes, set-up and tyre evaluation.
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