The wingers have been regarded amongst Europe's top players for much of their careers and made 48 Bundesliga appearances between them as Bayern once again won the title last season.
Both have been linked with lucrative moves to the burgeoning Chinese Super League in the past, but Davidsen hit out at suggestions that it was a place ageing players could go to see out the twilight of their careers.
"It's a misconception that makes me really angry when players in Europe believe they can freely choose the time to move to China. This was the situation three or four years ago but those times are over," he told Sport Bild.
"If Ribery had an offer two or three years ago from China then that was his chance but an ambitious Chinese team like Shanghai SIPG wouldn't sign him or Robben now.
"Why should a Chinese club sign a 33- or 34-year-old when they can get 27-year-old stars like Axel Witsel or Alex Teixeira — or Oscar at 25? Ribery and Robben have missed the chance if they had wanted to play in China. We no longer want these players."
Ribery is currently heading into his 11th year as a Bayern player, while next season will be Robben's ninth at the club.