Is it possible to add contribution note when renewing membership in (one of) the next release?
I would advise you to avoid changing the core files (php or template). You should write an extension that adds the field (in the buildform hook) and save it whilst processing the form.

However, It might be better to use other ways to save that information. The financial type for instance where you can create several, based on the bank (assuming it's the client bank) or use the check number or source (both existing fields in the contribution) if it's an information about the member's bank.