It was a problem in the certificate chain. The infrastructure guys repaired it and now I can log on.
Thank you very much for your help. I really appreciate.
I hope this could help someone. I had the same problem, moodle app wasn't able to reach the moodle site.
In the beginning I thought it was a problem with redirection from HTTP to the HTTPS, as Juan suggested, but even disabling it wasn't helping.
But thanks to this post I find out there was a problem with certificate CHAIN (not with certificate itself, but with the CA certificate).
I was able to find out with the help of online tools like ssl checker and similar.
The strange thing is that it was working correctly on iOS, the problem was only on Android devices (which are usually more tollerant....)
So, just in case you have the same problem (HTTPS: iOS -> OK && Android -> KO) just check ssl certificate chain (and fix it of course).