Not sure I understand the question fully, so perhaps let me try to answer this more generally. Generally speaking, err on whatever approach minimizes friction for your users (both buyers and sellers).

If you have a two-sided marketplace where a seller lists something (e.g. a commercial space available) for buyers (i.e. your clients), I think it's best to have this communication happen on the marketplace platform itself.

From a feature perspective, this might mean the buyers and sellers have message inboxes, as well as email notifications that notify them whenever a message (or reply) is received. You can even make things easier by inserting excerpts or full messages within the email notifications (and allow an easy reply-to-email for responses), but the entire conversation thread should still live on your platform's inbox.

Hope that makes sense and helps!