I hope this email finds you well. I've been working as a [[position]] at [[company]] for a few years now, and I've just started looking for a new opportunity. I'm extremely interested in [[company]], and I recently learned that you may have a contact there?
If there is any way that you could facilitate that connection, I would be extremely grateful - only if it's OK with you! I've attached my resume in case that's useful. Please feel free to cc me on any emails, and I am happy to follow up.
“ If you have a mutual connection/friend with someone you'd like to get to know, use some variation of this email template. You want to be using this only with warm contacts, ex-colleagues or friends who know you reasonably well!