collogue
Collogue (verb) means (dated) To gently persuade someone, or to flatter them.
Etymology
First recorded in the 1590s (as colloguing), presumably from colleague (“to associate”) and French colloque (“secret meeting”), from Latin colloquium (English colloquy), possibly influenced by dialogue. This ultimately goes back to Latin collega (“a partner in office”) and Ancient Greek λόγος (lógos, “speech; oration; discourse”), perhaps partly by way of Latin loquor (“to speak”).