Both can be correct, but I would expect that the first version is the one that you would actually want most of the time.
In the first version, "I'll let you know when I have more information", there are two time points. At time T (now) you don't have more information. You are promising that at some time T+1, you will have more information, and at that same time T+1 you will inform them of this information.
In the second version, "I'll let you know when I will have more information", there are three time points. At time T (now) you don't have more information. At some time (T+1) you will have a schedule. This schedule gives a time (T+2) at which you will have more information. You are promising that at time (T+1), when you have the schedule, you will inform them of the schedule.
The choice of wording depends on a few things, including:
- Intent: Are you trying to nudge for a meeting this week?
- Region/dialect: Different parts of English-speaking world use
different wording for politeness.
- Relationship: Is the addressee a peer or a superior?
As a Canadian English speaker, I would say either of your sentences can be used politely, but a few tweaks are needed:
- "in this week": This is unnatural. Use "this week" or "during the week": both are equivalent.
- Question form: Typically, a question form might be seen as less pushy. (Tied to factors 2 and 3 above.)
- Replace "when" with "if": This can only be done if you are willing to give the other person an option to not meet this week. (Tied to factors 1 and 3 above.)
- "your convenient time": This is unnatural. You would use "time convenient for you" if you want to stress on the addressee's convenience or "a convenient time" if you want to talk about a time convenient to both of you.
Putting all this together, one can arrive at many possible sentences. Here are some examples.
I would use this only with someone over whom I have authority:
Let me know when you are free during the week to discuss.
I would use this for a peer or superior if I wanted to give them the option to postpone:
Could you please let me know if you have time to discuss this week?
This is a clever construction that forces the other person to commit to a time this week, but you still make it sound like you are leaving it up to her/him. I would pick one of these if I wanted to push someone with whom I had a formal relationship:
Let me know what time is convenient for a discussion this week.
Could you please let me know what time is convenient this week for a discussion?
Many other answers are possible. We would really need better context to narrow it down.
Best Answer
No! It should be...
Here, the word let is used as to notify you when something happens in future (here, when that person is free). The verb were refers to past where future notification cannot happen in this context.