I'm on the verge of...

Meaning

I'm about to...

Examples

• John: How's the report coming along?
• Alice: <b>I'm on the verge of</b> completing it. Just a few more edits.
• John: Great! Let me know when you're finished.
• Alice: Will do. I expect to send it in the next hour. <b>I'm on the verge of</b> submitting it.