Both wingers have been linked with moves to Asia in the recent past, but have opted to remain in Europe.
Neither have offered any indication that they intend to head to the Far East any time soon, but they have been warned that the opportunity to take advantage of such riches may have passed them by.
Ribery and Robben are now 34 and 33 years of age respectively, with the CSL eager to move away from veteran performers and towards players with potential to contribute in the present and future.
Davidsen told Sport BILD: “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.
“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?”
Robben claimed in January that he would never rule out a move to China, saying: “My family comes first, but the life experience, living elsewhere - in the USA, in China - might come. But maybe not. Maybe I'll go back home [to the Netherlands]. I do not rule out anything.”
He was, however, speaking after committing to a new 12-month contract at Bayern and will be going nowhere until at least the summer of 2018.