I agree with Gary: you should use "would" rather than "will". Alternatively you could say "I am quite willing to ...." "Willingly", used this way, means "cheerfully consenting or ready". For example, "he is a willing worker", "she went with him willingly". So your use of the word here makes perfect sense. Отлично!

The sentence structure is OK. It would be better to use 'would' rather than 'will' - as 'will' sounds like you are insisting on a conversation, whereas 'would' means that you would be happy, if I am too.