Tvheadend

Use a VLC or Kodi capable device with speakers.
Eg.: I use my iPhone for listening radio in the bathroom.

Thanks for your suggestion. You did hit my point, but would like the device to be the input for my stereo, to be able to use that. I know I am probably asking for something that does not exist.
I have thought of a satellite receiver, but that would require an extra satellite cable and my dishes lnb has no spare cable slot.
Is a dreambox for instance kodi capable ?

Could your stereo receive input through HDMI?
If yes, google on Raspberry Pi with OpenELEC or OSMC (Kodi).
If no, google on Raspberry Pi with Hifiberry or derivates and the operating systems above.
Or use a tablet/mobile for input with VLC or Kodi.

I thought of a raspberry (have a type 1 lying around). Soundcard with analog output should be possibel. If I run kodi it needs a screen and a remote.
I don't quite understand what you mean by "Or use a tablet/mobile for input with VLC or Kodi." Do you mean to operate kodi (like switching stations) by a mobile ? I am getting curious now.

With Kodi remote you don't need a screen. You can switch to a radio station with the mobile remote. (Kodi on RPi, remote on mobile).

A mobile/tablet connected with 3,5" jack cable is not enough for radio quality? (Mobile connected to stereo with jack) And on the mobile/tablet you could run Kodi/VLC that could connect to tvheadend.

Is it helped?

I have a cheap - £60 a couple of years ago? - Android tablet that I connect to Bluetooth stereo speakers. It's fast enough to run Kodi, although streaming HD video would be too much... but it's plenty capable of streaming FLAC/MP3 over 802.11n (although wireless is a problem on many cheap tablets). I can also then stream IP radio streams (e.g. through Tune In), Spotify or - of course - via tvheadend.

You could do the same with any old Android or iOS phone - even one off eBay for next to no money.

A Bluetooth-to-3.5mm adapter is cheap... after that, it depends on outputs/inputs, but a 3.5mm out on the headphone socket should connect through to an AUX input on your stereo with some adapters.

You could define a specific user on tvh who only has access to the radio tags, if you want to simplify things. And you can then use the touchscreen to navigate - which is difficult on a 10cm screen, admittedly! - or something like Yatse or the official Koi remote to control things.

Both Andras and Prof Yaffle thanks for clearing things up. I do have no idea about sound quality produced this way, but if I read your messages well it should be sufficient, and I'm not a high fidelity freak. FM is a bit troublesome, that's the reason to think of satellite.
I now understand the idea, with for the time being two questions left : If I run kodi on a pi, how does it receive signals from 'remote' on phone or tablet and second is the remote on such a device an app ?

I have no or little experience with smartphones. I still use one pc running openelec/kodi for which I build a 'home brew' lirc receiver for a remote. Openelec/kodi on my raspberry model2 is totally controlled by the tv remote through CEC. That's why i do not yet understand communication between kodi and mobile device.

I do like the idea of seperate user on tvh for radio, great idea.

I will keep my eyes open for an old android or ios phone or tablet. It also seems to be possible to run kodi on some linux-based satellite receivers. I will investigate that further, but i'm on my way. Thanks for helping me.

Wifi. You could theoretically use a tunnel over the cellular network and back through a router and a wired LAN, but...

And yes, it's an app. For Android, for example:

https://play.google.com/store/apps/details?id=org.xbmc.kore

https://play.google.com/store/apps/details?id=org.leetzone.android.yatsewidgetfree

... although other choices exist for other platforms.