Dr Helmut Marko is urging Honda to take "more risk" in order to produce a more powerful engine for Red Bull.
Amid rumours the team could lose him to Mercedes, Max Verstappen said the 2019 Red Bull package is "not bad" but must take "a big step with the engine".
Marko said Red Bull is happy with Honda.
"The engine is incredibly reliable — we haven’t had a failure," he said. "Everything Honda has promised to us has been fulfilled.
"But our previous updates did not bring as much benefit as those at Mercedes and Ferrari," said Marko.
"In the future, we would like to see a little more risk and hope for a power increase.
"We would rather start from the back with a stronger engine, because if Max starts at the back, a thrilling grand prix is guaranteed," he added.
Verstappen actually won the Austrian GP last year with a Renault engine, but says he would need "luck" to repeat that in 2019.
"But I have a lot of faith in the car and the team and everything is possible on a perfect day," he said.