Thank you all for your help and advice. I am still using
Mendeley and, unfortunately, their Desktop version, which supports LibreOffice, rarely receives updates and it will not receive any new features. They developed a new version, Mendeley Reference Manager, which does not support LibreOffice.
Zotero does support LibreOffice, but it did not work on my system for I do not have Java installed. Now my question is, and I know you might not have an answer for it, does Mendeley require Java too, but Java is embedded in their installer? What if I migrate to Zotero and install Java JRE 8 and install OS Armor (I am using McAfee and F-secure on my systems and OS Armor seems to play well with the two solutions)?