Learn English – Is it correct to write: “I would appreciate it if you could inform me when you could contact the manager” in a formal email?

Depending on the size of the vendor, your assumption may not be entirely warranted. If there are several people who may potentially receive the email at the distributor (as may happen with a shared departmental mailbox) the person who receives your email may not be aware of all the facts.

Accordingly, it may be wise to refer to the previous email at the beginning of your email (..."per the email from Mr. Customer sent yesterday regarding WidgetCo Widgets") and reiterate any key facts that you need to rely upon to make your point (..."we require, as stated previously, forty-two Widgets within a week").

By referring unambiguously to the email at the beginning, you can ensure that the person who receives your email will be reminded (if they had forgotten); will research (if they are a different person who did not initially receive the other email); or will delegate to the appropriate person (if someone else has the responsibility for this transaction).

Even if it is the same person, the phrasing mentioned above should be usable; it never hurts to ensure that your intentions are clear.

Good luck!

Actually, I want to know is perfectly valid. If it’s politeness you’re trying to achieve, you could say I would like to know.

This transforms what might have been interpreted as a demand into a request.

An alternative word would be enquire, such as in I would like to enquire.