No.  The only way it goes away is if you enable cellular data for the app in question

The app needs to connect to the internet to acquire information. If you have Cellular Data turned off the app can't get the information it needs. You might as well not start the app or turn Cellular data on.

"The app needs to connect to the internet to acquire information."

obviously you don't have this problem and do not understand this problem.

I use audible to listen to audiobooks that I have bought, downloaded and put on my iPhone so the whole audiobook is ON the iPhone.  There is no reason whatsoever for audible to pester me many times a day with "cellular data is turned off for Audible" - I've set preferences for audible to use wifi only.

"f you have Cellular Data turned off the app can't get the information it needs."

obviously I do have all the information it needs.

"You might as well not start the app or turn Cellular data on."

Cheee - please learn exactly what the problem is that a person is asking about rather than provide snide comments.

I've resorted to using iTunes to play the audible books. It is not as nice as the audible app but it works without dozens of irritating popups.

I keep complaining to audible as yes this is an apple iPhone but it is THEIR app and why does it beg for cellular all the time? Very irritating.

I keep hoping for a fix.

I did figure out a fix for the audible app problem. It did not do this in past releases. I was able to get an old iPod touch and load the app on it - the flag says something about this being an older iPod so it will have to load an older version, is that OK? Yes indeed. I deleted the audible app from the iPhone AND from the mac app library. Backed up the iPod, which then put the older version onto the computer. Added the old app to the iPhone and Bob's your uncle. It will ask periodically for the cellular but not that constant, overwhelming number of popups.

Awkward but it works.