The www.motorsport.com website reported the acclaimed designer would stand aside to focus on technical matters, with Wheatley returning to Britain from Audi's factory in Switzerland.
"The team will not be engaging in media speculation about its senior leadership team," Aston Martin said in a statement.
"Adrian Newey continues to lead the team as Team Principal and Managing Technical Partner."
Audi said they were aware of the media reports.
"There is no official update from our side at this point in time and we do not comment on speculation," said a team spokesman.
Silverstone-based Aston Martin have yet to score a point or finish either of the two grands prix this season, with their new Honda power unit lacking performance and producing heavy vibrations.
Two-time world champion Fernando Alonso retired from last Sunday's Chinese Grand Prix after saying he was losing feeling in his hands and feet. On board footage from the race in Shanghai showed Alonso taking his hands off the steering wheel whenever possible to ease the pain.
The team are owned by Canadian Lawrence Stroll, whose son Lance races as Spaniard Alonso's teammate. They finished seventh last season with Mercedes engines.
Newey took over as principal this season with previous incumbent Andy Cowell, a former Mercedes engine boss, moving into a strategy role.
Newey, whose cars have won 14 drivers' and 12 constructors' titles for three different teams, joined Aston Martin from Red Bull last year as a shareholder and tasked with building a winning car.
The softly-spoken Briton, 67, had worked closely with former team boss Christian Horner and Dutch four-time world champion Max Verstappen at Red Bull, but his promotion as Aston principal came as a surprise.
Wheatley, who also worked with Newey at Red Bull previously and was sporting director when he left, joined Audi's predecessor Sauber in April last year.
Any further move would likely involve a long period of 'gardening leave' before he could start work at any rival outfit.
Audi also have former Ferrari principal Mattia Binotto overseeing the F1 project.
The next grand prix at Japan's Suzuka circuit on March 29 is a home one for Honda but unlikely to bring any relief for the Japanese manufacturer.