Dr Helmut Marko revealed that some rival teams are offering to pay twice as much as Red Bull team.
In Monaco, Ferrari team boss Marco Mattiacci denied reports he had offered Newey dozens of millions of dollars if the highly-respected engineer moved to Maranello.
Dr Helmut Marko is quoted by Kleine Zeitung newspaper as revealing that some rival teams are offering to pay "about double" in order to attract Red Bull staff.
"And we pay our people quite decently," he said.
Newey is the obvious main target. Marko told the newspaper that the Briton received an offer from the mouth of Mercedes team chairman Niki Lauda.
And the Kleine Zeitung report added: "Marko said Ferrari president Luca di Montezemolo went to Barcelona two weeks earlier to present his offer (to Newey)."
Marko said: "Newey has decided to stay with us at Red Bull until further notice."