Hi seilemor,
I had the exact same issue - no export of learning suggestions available in ASM GUI.
I wrote a script in Python using f5-common-python SDK which allowed me to export ASM learning suggestions into an Excel spreadsheet with almost all the information you can find in GUI. To export just a simple list of suggestions is pretty easy. Things get complicated when you need to include details about every different type of an attack. But it's worth the effort.
Start here with SDK documentation:
https://f5-sdk.readthedocs.io/en/latest/apidoc/f5.bigip.tm.htmlmodule-f5.bigip.tm.asm
The current version of the SDK is not complete, for example it does not support Requests and Violations, so I extended it myself, have a look here for inspiration:
https://github.com/F5Networks/f5-common-python/issues/1486
Hope it helps.