Newey, 65, has been with Red Bull since 2005 and has played a key role in all of the team's 13 world titles -- seven drivers and six constructors -- since 2010.
However, he is believed to have become unsettled at the team ever since team principal Horner was accused of sexual harassment and inappropriate behaviour by a female employee.
Horner was cleared of wrongdoing by an internal investigation carried out by Red Bull's parent company before the employee was then suspended. She is appealing that decision.
After Germany's Auto Motor und Sport first reported Newey's position on Thursday, the BBC claimed they had "independently verified (the information) with high-level sources close to Red Bull and Newey".
They confirmed that his desire to leave stems from his unhappiness over the Horner situation which has sparked a power struggle at Red Bull.
World champion driver Max Verstappen has also become frustrated with the situation.
His Red Bull future was thrown into doubt last month after his father, Jos, said the team was in danger of being "torn apart" if Horner remained its principal.
A Red Bull team spokesman later Thursday said they were "unaware" of Newey's apparent desire to leave.
"Adrian is contracted until at least the end of 2025 and we are unaware of him joining any other team," he told AFP.
Last year, Verstappen and Red Bull produced the most dominant season in F1 history, with the Dutchman winning 19 of the 22 races and the team all but one.
This season they have won four of the first five races.
Newey has also worked with championship-winning teams at Williams and McLaren in his long career.
According to the BBC, he has been strongly linked with a switch to Ferrari.
