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.
But the rumours were strong enough that Red Bull issued a media statement quoting Newey as saying: "I remain committed to Red Bull for the foreseeable future."
The fact Red Bull did not single out Ferrari's reported interest in the statement could be because it was not the 55-year-old's only offer.
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.
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."