Former world champion Niki Lauda said the Scot would be a good solution because of his experience.
Red Bull represent the 33-year-old's best chance of staying in the sport after a decade with Williams and McLaren.
Red Bull Racing owner Dietrich Mateschitz has given a fresh boost to David Coulthard's hopes of staying in Formula One next year.
The Scot is looking for a drive after McLaren signed Colombian Juan Pablo Montoya from Williams for 2005.
India doesn't have a legacy in Formula One drivers but Narain Karthikeyan is a "talented driver who could have done wonders had he be racing for any other team" than minnows Hispania Racing (HRT), feels former multiple Grand Prix winner David Coulthard.
Former Formula One ace David Coulthard wants to go flat out when he drives Red Bull car on the Bandra-Worli Sea Link on Sunday, but is constrained by the speed limit the authorities have fixed.
Ferrari's Michael Schumacher finished fourth in a damaged car, ending his record run of 19 successive podiums.
The Australian will take the place of young Austrian Christian Klien at the team.
The Scot believes his former McLaren team mate Kimi Raikkonen could yet emerge as Formula One champion this season.\n
Maharashtra State Road Development Corporation (MSRDC) would consider action against organisers of the exhibition event where former British F1 racer David Coulthard drove a Formula One car on the Bandra-Worli Sea Link allegedly beyond permissible speed limits.
Following rules does not seem to be one of the virtues of former Formula One ace David Coulthard, who defied the speed limits and zoomed across the Mumbai sea-bridge at a breakneck speed of 260km per hour.
Formula One's newest circuit in Abu Dhabi could prove trickier this weekend than any other track introduced in recent years, according to former racer David Coulthard.
Formula One's ruling body should have punished Brazilian Nelson Piquet for the Renault race-fixing controversy, former driver David Coulthard says.
"To expect them to win a Grand Prix is a pipe dream at this moment in time," said the Scot, winner of 13 races with Williams and McLaren.
Briton David Coulthard has visited Williams bosses in a bid to convince his former employers to take him back next year.
The McLaren driver has called for a re-think on rules that allow the bottom six teams to run a third car on Fridays at Grand Prix weekends.
Lewis Hamilton's Formula One switch from McLaren to Mercedes next year is an essential step that could be the making of him as a man, former McLaren driver David Coulthard said on Saturday.
Retired British driver David Coulthard is on standby for a Formula One comeback if either of Red Bull's drivers are unable to race in the first two Grands Prix of the season, the team said on Wednesday. A spokeswoman said the 37-year-old Scot, in Melbourne as a pundit for BBC television, was their official reserve driver for Sunday's Australian season-opener and the following race in Malaysia.
David Coulthard warned that Formula One drivers could go on strike if their safety concerns are ignored.
Former Red Bull driver David Coulthard on Friday said Force India's stunning show in the second half of the 2009 Formula One season is no fluke and the country should be proud of the Vijay Mallya-owned outfit's spectacular achievements.
The Scot is looking to get his act together in the next F1 race at Monaco and make up lost ground.
"The reality check is a race weekend so there is nowhere to hide from that," said the Scot.
Tail-enders Force India could be Formula One's surprise package this season with the help of McLaren and Mercedes, former driver David Coulthard said on Monday.
Former Grand Prix winner David Coulthard announced on Thursday he would retire from Formula One at the end of the year after 15 seasons in the sport. The 37-year-old Scot, the oldest driver on the starting grid, said he would remain actively involved after that as a consultant to his Red Bull team and did not rule out an occasional test drive.
Mumbai's Formula One fans have a treat in store. Ace driver David Coulthard is scheduled to drive down the Rajiv Gandhi Bandra-Worli Sea Link at blinding speed in a Red Bull racing car on October 11.
No woman has competed in Formula One since 1976 but organisers of the 'W Series' hope to provide a platform for them to develop skills before taking on the men further up the motorsport ladder. The idea of an all-female series is not new but has been controversial in the past, with top women racers adamant they want to compete against the men rather than be separated.
Ferrari's new champion Kimi Raikkonen was fourth on the timesheets.
The Formula One world champion sees McLaren as a potential threat to Ferrari's domination this season after David Coulthard's impressive times in recent testing.
British teenager Oliver Rowland will have a Formula One test with McLaren after collecting a coveted Autosport award previously won by the likes of Jenson Button and David Coulthard.
Formula One drivers will seek a clarification of the rules before Sunday's Italian Grand Prix after stewards stripped Lewis Hamilton of victory in Belgium last weekend for cutting a chicane. The ruling outraged many fans and dominated the first day at Monza, with drivers divided on the justice of the penalty while other leading figures expressed concern for the fundamentals of the sport.