Adrian Newey said no when Ferrari asked if he wanted a job with F1's famous Italian team, according to reports on Thursday.
But the 52-year-old could have moved to Ferrari, an online report by the BBC said.
"Of course, Adrian is one of the best, if not the best, in F1," confirmed Ferrari team boss Stefano Domenicali in an interview with La Gazzetta dello Sport.
"We joke a lot about the possibility but I have the impression he is happy in England and that he will stay at Red Bull," he added.
Domenicali's Red Bull counterpart Christian Horner added: "It's understandable why any team in F1 would be interested in Adrian but he is very much enjoying life at Red Bull and I'm sure he'll be here for years to come."
It's understandable why any team in F1 would be interested in Adrian
Newey told F1 Racing magazine earlier this year that the recent Ferrari approach was not a one-off.
"I've had offers from Ferrari in the past and I've considered them seriously. But F1 is a people sport, not a marque sport.
"It's flattering if people rate the work I do but that's not why I get out of bed in the morning. I do it because I enjoy the design challenge of F1," added Newey.