There's okurigana at the end but for the kanji 口 used onyomi reading "ku" instead of "kuchi"
大辞泉 dictionary lists this as possibly being ateji.
The verb くどく probably shares its origin with the mimetic word くどくど (repetitively, at great length, etc.). Both would have existed prior to being written.
The idea is that the kanji 口 and 説 were then chosen as a way to represent the existing word, ignoring how one would read them if the idea was to make a word from 口 and 説 from scratch.
This is not unusual, and represents a source of many exceptional readings.
The dictionary isn't absolute in its assessment though, leaving open the possibility of some other origin of the orthography.