With Italian Jarno Trulli having every chance of his third successive front row start after finishing a close second in Saturday's first qualifying session, technical director Mike Gascoyne spelled out the team's ambitions.
"Yet again we have a car in second position, but the team is now looking to achieve more than that," the Englishman said. "We have to consolidate Jarno's starting position and aim to score at least our second podium."
Final qualifying is on Sunday before the race.
Trulli finished runner-up to Renault's Championship leader Fernando Alonso in the Malaysian Grand Prix for Toyota's first top-three finish since they came into the sport in 2002.
"I'm performing well because the team is doing a great job," said Trulli, whose teammate Ralf Schumacher was only 11th in qualifying after losing time at turn eight.
The German had been the second quickest driver in final practice when fuel loads are low and the cars closest to qualifying trim.
"It looks like if we can get everything right during the weekend we can get performance as well," said Trulli. "We have to keep up this momentum and carry on working because it's not only going to be an interesting race but an interesting season for us."
Toyota have spent an estimated $1 billion since they entered Formula One but until this year had scant reward for their labours. Now they are second in the Championship after two races and contenders at last.
"We must be satisfied because we could never have expected to be here when we started our relationship with Toyota last year," said Trulli, who was Alonso's teammate at Renault last year and won the Monaco Grand Prix.
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