[ByTheWay]

Ok, I think i've got it. It's a bit like - 'by next week I will have typed the report'. Like a past participle to indicate an action that will be completed at some time in the future, hence the reason why it does not have a past tense.

今時間がないので来週会ったとき話しましょう

means, I don't have time right now, but by next week we will have met and conversed.